16. Q16d
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Similar Question 1
<p>Expand and simplify.</p><p><code class='latex inline'>(2x-5)^2</code></p>
Similar Question 2
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle 2(3 m-n)^{2}-3(2 m-5)(m+3) </code></p>
Similar Question 3
<p>Expand.</p><p><code class='latex inline'>\displaystyle 2(3 m+1)^{2} </code></p>
Similar Questions
Learning Path
L1 Quick Intro to Factoring Trinomial with Leading a
L2 Introduction to Factoring ax^2+bx+c
L3 Factoring ax^2+bx+c, ex1
Now You Try
<p>Simplify. <code class='latex inline'>\displaystyle -7(y-2) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (4a + 3b)(5a - 3b) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(a+4)^2</code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle (3 a-b)(3 a+b) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(4x + 5)(3x - 2)</code></p>
<p>Expand and simplify.</p><p> <code class='latex inline'>(x+y)(2x+3y)</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (x+2 y)(x-2 y)+(2 x+y)^{2} </code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle (1-6 y)(-3) </code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle 4(1-2 x+5 y) </code></p>
<p>Find the product.</p><p><code class='latex inline'>\displaystyle (x+1)(x+5) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (5 m+2 n)(4 m-3 n) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(x+2)(x+5)</code></p>
<p>Expand. Verify the solution by substituting 1 for the variable.</p><p><code class='latex inline'>\displaystyle (x-7)(x+1) </code></p>
<p>What binomial product does each model represent?</p><img src="/qimages/15511" />
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (x-5)(4 x+3) </code></p>
<p>Expand.</p><p><code class='latex inline'>\displaystyle (a-5)^{2} </code></p>
<p>Expand and simplify</p><p><code class='latex inline'>3(2x+1)^2-2(3x-1)^2</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(x-2)(4x-6)</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(2x - 3)(2x + 3)</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (3 y+1)(y+2) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'> \displaystyle (7m - n)^2 </code></p>
<p>Find the product.</p><p><code class='latex inline'>\displaystyle (2 a+b)(a-3 b) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>2x(x-5)</code></p>
<p>Simplify</p><p><code class='latex inline'>\displaystyle 2[4 + 3(x - 5)] </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle -3(5 a-4)(5 a+4)-3 a(a-7) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(3x=7)(6X-5)</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle k(2k - 1) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle 2(3 x+1)^{2}+3(2 x-1)(2 x+1) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (1-6 t)(4+5 t) </code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle -(2 a-4 b-c) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle 2t(3t -4)+t(2t +5) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(5c-d)(5c+d)</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>2(3x+4)^2-3(x-2)^2</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (x-1)(2 x-1) </code></p>
<p>How do you know that the product will be quadratic when you expand an expression such as </p><p><code class='latex inline'>(2x+3)(3x-2)</code>?</p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle 4(5 s+t)(5 s-t)-6\left(3 t^{2}-t\right) </code></p>
<p>Find the product.</p><p><code class='latex inline'>\displaystyle (x-6)(x+3) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (4m + n)^2 + 2(m -2n)^2 </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(y+2)(y+5)-(y-2)(y-5)</code></p>
<p>Determine if the functions in each pair are equivalent.</p><p><code class='latex inline'>f(x) = 5(x ^2 + 2x - 3) - (2x + 5)(-x + 1)</code>, <code class='latex inline'>g(x) = 7x^2 + 13x - 20</code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle (4 a+3)(5 a) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle 12-2(3 y-2)(3 y+2)-(2 y+5)(2 y+5) </code></p>
<p>Expand. Verify the solution by substituting 1 for the variable.</p><p><code class='latex inline'>\displaystyle (x+2)(x-5) </code></p>
<p> Use the distribution property to multiply the following numbers.</p><p><code class='latex inline'> \displaystyle -987 \times (-201 ) </code></p>
<p>Expand and simplify. </p><p><code class='latex inline'>\displaystyle 5(2 y+1)-(5 y-2) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle \left(3 x^{2}+2 y^{2}\right)\left(3 x^{2}-2 y^{2}\right) </code></p>
<p>Use the Distributive Property to rewrite each expression. Then evaluate. <code class='latex inline'>\displaystyle (4+5) 6 </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(x-4)(x-2)</code></p>
<p>Expand and simplify. </p><p><code class='latex inline'>\displaystyle 3\left(3 z^{2}-5 z-4\right)+2 z(4 z-1) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(x +5)(x + 4)</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'> \displaystyle (3a - 8c)(3a + 8c) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle -8\left(x^{2}-5 x+7\right)+5(2 x-5)(3 x-7) </code></p>
<p>Use the Distributive Property to rewrite each expression. Then simplify.</p><p><code class='latex inline'>\displaystyle (4-3 m) 8 </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(4x - 2y)(5x + 3y)</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle \left(y^{2}-2\right)\left(y^{2}+2\right) </code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle (4 t-5 s)^{2} </code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle 6(3 a-4 b-9) </code></p>
<p>Expand and simplify</p><p><code class='latex inline'>3a(a-5)-(2a+1)(a-7)</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>2m(3m+1)+(m-4)(5m+3)</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle 3(x-4)+5(x + 6) </code></p>
<p> Use the distribution property to multiply the following numbers.</p><p><code class='latex inline'> \displaystyle -213 \times 999 </code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle (2-3 t)^{2} </code></p>
<p>Expand.</p><p><code class='latex inline'>\displaystyle 3(4 x+3)(4 x-3) </code></p>
<p>Expand the following.</p><p><code class='latex inline'>\displaystyle -2(4 y+1)(y-3) </code></p>
<p>Expand and Simplify.</p><p><code class='latex inline'>\displaystyle (y+4)(y-3)+(y-2)(y-3) </code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle -5\left(2 x^{2}+3 x y-y^{2}\right) </code></p>
<p>Expand and simplify.</p><p> <code class='latex inline'>(8x-y)(7x+2y)</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle \left(4 x^{2}+3 y^{2}\right)^{2} </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(5y-2)^2</code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle (1+5 m)(1-5 m) </code></p>
<p>Find the product.</p><p><code class='latex inline'>\displaystyle (x+4)(x+3) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'> \displaystyle -2(-2x + 5)(3x + 4) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle 3(3 m+1)(m-4)-4(2 m+3)(2 m-3) </code></p>
<p>Expand and simplify each expression.</p><p><code class='latex inline'>(x+3)^3</code></p>
<p>What binomial product does each model represent?</p><img src="/qimages/15512" />
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle 4(2 x+1)^{2}-2(3 x-7)^{2} </code></p>
<p> Expand <code class='latex inline'>(a+b)^4</code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle 2 a(3-4 b+5 a) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(2x+5)^2+(2x-5)^2-(2x-5)(2x+5)</code></p>
<p>The formula for the surface area of a rectangular prism is <code class='latex inline'>SA = 2(lw + hw + lh)</code>. Apply the distributive property to write this formula in another way.</p>
<p>Expand and simplify each expression.</p><p><code class='latex inline'> \displaystyle (3x^2 + 6x - 1)^2 </code></p>
<p>Expand.</p><p><code class='latex inline'>5(x+2)</code></p>
<p>Use the Distributive Property to rewrite each expression. Then simplify. <code class='latex inline'>\displaystyle 2(x+4) </code></p>
<p>Expand.</p><p><code class='latex inline'>\displaystyle (3 t+1)(3 t-1) </code></p>
<p>Expand and simplify.</p><p> <code class='latex inline'>-2(x+3y)(2x-y)</code></p>
<p>Expand. Verify the solution by substituting 1 for the variable.</p><p><code class='latex inline'>\displaystyle (4+x)(7-x) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(c-1)^2</code></p>
<p>Find the product.</p><p><code class='latex inline'>\displaystyle (b-1)(b-5) </code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle -6 x(3 x-6 y-9) </code></p>
<p>Expand.</p><p>a) <code class='latex inline'>\displaystyle -5(p^2 + 3p - 1) </code></p><p>b) <code class='latex inline'>\displaystyle 4b(b^2 - 2b + 5) </code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle (2 m+7)^{2} </code></p>
<p>Expand and simplify each expression.</p><p><code class='latex inline'> \displaystyle (x + 6)(x + 3)(x - 6)(x - 3) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle \left(3 y^{2}-4\right)^{2} </code></p>
<p>Expand and simplify.</p><p> <code class='latex inline'>(5m-7n)(5m+7n)</code></p>
<p>Expand. Verify the solution by substituting 1 for the variable.</p><p><code class='latex inline'>\displaystyle (2-y)(3-y) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(x-2)(7x+3)</code></p>
<p>Determine if the functions in each pair are equivalent.</p><p><code class='latex inline'>f(x) = (x + 5)^2 - 2(3 - x)(x + 1)</code>, <code class='latex inline'>g(x) = -2(-x^2 + 4x - 8) + (x + 4)^2 - 6</code></p>
<p>Determine the missing terms.</p><p><code class='latex inline'>(k-2)(k+1)=\square+\bigcirc-2k-2</code></p>
<p>Expand.</p><p><code class='latex inline'>\displaystyle 2(3 m+1)^{2} </code></p>
<p>Expand.</p><p><code class='latex inline'>\displaystyle (2 x-3 y)^{2} </code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle (m-7)(m+7) </code></p>
<ol> <li>a) Verify that <code class='latex inline'>\displaystyle (x+6)(x+2) \neq x^{2}+12 </code> by substituting 1 for <code class='latex inline'>\displaystyle x </code>. b) Expand <code class='latex inline'>\displaystyle (x+6)(x+2) </code> correctly.</li> </ol>
<p>Expand. </p><p><code class='latex inline'>\displaystyle (3 x-1) 2 </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle 4 x(2 x-3)-x(3 x-1) </code></p>
<p>Expand. Verify the solution by substituting 1 for the variable.</p><p><code class='latex inline'>\displaystyle (x+7)(x+7) </code></p>
<p>Simplify each expression. If not possible, write simplified.</p><p><code class='latex inline'>\displaystyle (2-4 n) 17 </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle \frac{2}{3}(3a + 1) + \frac{1}{2}(4a -1) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (-3 a+4 b)(2 a+3 b) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'> \displaystyle -(5x - 8y)(5x + 8y) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle \frac{1}{2}(6 +3p) - \frac{3}{4}(8 - 10p) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(4x-6)(4x+6)</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'> \displaystyle (2c + 9d)^2 </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (m +3)(m + 7) </code></p>
<p>Expand and simplify</p><p><code class='latex inline'>\displaystyle\begin{array}{c}2\left(x^{2}-5\right)-7 x(8 x-9)\end{array}</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>-a(2a+3)+2(a+4)(3a+4)</code></p>
<p>Expand and simplify.</p><p> <code class='latex inline'>(-3d+5)^2</code></p>
<p> Expand and simplify <code class='latex inline'>(3-2x)(x+2)</code></p><p> Evaluate for <code class='latex inline'>x=-4</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (x- 4)(x + 4) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (x-1)^{2} </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>-4[3-2(c+5)-4c]</code></p>
<p>Expand.</p><p><code class='latex inline'>-4(y-3)</code></p>
<p>Expand each expression.</p><p><code class='latex inline'> \displaystyle (a + b)^4 </code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle -2(3 x-7) </code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle (3 y-2)(3 y+2) </code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle (x-6)^{2} </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(3x-2y)(5x+4y)</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (2 y-3)(2 y+3) </code></p>
<p>Expand and simplify.</p><p>a) <code class='latex inline'>\displaystyle 2(q - 5) + 4(3q +2) </code></p><p>b) <code class='latex inline'>\displaystyle 5x(2x -4) -3(2x^2 +8)</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'> \displaystyle (2x + 6)^2 </code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle (y+1)^{2} </code></p>
<p>Multiply each of the following,</p><p><code class='latex inline'>\displaystyle (20-2)(20+2) </code></p>
<p>Expand and Simplify.</p><p><code class='latex inline'>\displaystyle 3(2 a+3)(2 a-1)-4\left(a^{2}-7\right) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'> \displaystyle (e - 10)(e + 10) </code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle (3 x+2)^{2} </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (3 a-5)(3 a+5) </code></p>
<p>Find the product.</p><p><code class='latex inline'>\displaystyle (y+5)(y+6) </code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle (m-3)^{2} </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (x+2 y)^{2} </code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle (4 y-3)^{2} </code></p>
<p>Expand and simplify.</p><p> <code class='latex inline'>(x+2y)(3x+y)</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle 2(1-3 t)^{2}-4(1-3 t)(1+3 t) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle 6(a+ 3)-2(a-5) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(2x-5)^2</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle -2 x(3 x-4)-x(x+6) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle \left(y^{2}-1\right)^{2} </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'> \displaystyle (x - 15)(x + 15) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle x(3x + 1)(2x - 5) </code></p>
<p>Expand and simplify</p><p><code class='latex inline'>\displaystyle\begin{array}{c}3 x(2 x-3)+9(x-1)-x(-x-11)\end{array}</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle 2(3m + 1)^2 </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (m-8)^{2}-(m-1)(m+1) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle 2(3 x+2 y)(3 x-2 y)-3(3 x-y)^{2} </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(x+4)(x-2)+(x-1)(x+5)</code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle (2 x+3 y)(2 x-3 y) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle -3(5 n-4)^{2}-5(5 n+4)^{2} </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(x+2)^2</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (h + 5)^2 </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(3x-2)(4x+5)</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(x+1)^2</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(7x-5)(7x+5)</code></p>
<p>Expand. Verify the solution by substituting 1 for the variable.</p><p><code class='latex inline'>\displaystyle (a+9)(a-5) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(3a-5b)^2</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle 5(3 t-4)(2 t-1)-(6 t-5) </code></p>
<p>Expand and simplify each expression.</p><p><code class='latex inline'>[(x+2)(x-2)]^2</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'> \displaystyle (b + 6)(b - 6) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle -5(x -4)^2 </code></p>
<p>Expand and Simplify.</p><p><code class='latex inline'>\displaystyle 4(2 x-1)(x+3)+3(x-2)(3 x-4) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (3 x+y)(x+4 y) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (2y -1)^2 + (y + 2)^2 - (1-2y)(1+ 2y) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle \left(x^{2}-2 y^{2}\right)^{2} </code></p>
<p>Expand and simplify.</p><p> <code class='latex inline'>(6x-5y)(6x+5y)</code></p>
<p> Use the distribution property to multiply the following numbers.</p><p><code class='latex inline'> \displaystyle 15 \times 12 </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(3x-2)(x+1)</code></p>
<p>Find the product.</p><p><code class='latex inline'>\displaystyle (x-4)(x-3) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle \left(x^{2}+1\right)^{2} </code></p>
<p>Expand and Simplify.</p><p><code class='latex inline'>\displaystyle -2(y-1)(y+4) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(x+2)(x-1)</code></p>
<p>Find the product.</p><p><code class='latex inline'>\displaystyle (t+10)(t-10) </code></p>
<p>Which pairs of functions are equivalent?</p><p><code class='latex inline'>b(t) = (3t + 2)^3</code> and <code class='latex inline'>c(t) = 27t^3 +54t^2 + 36t + 8</code></p>
<p>Error Analysis Describe and correct the error made in finding the product.</p><p><code class='latex inline'>\displaystyle \begin{aligned}(x-2)(3 x+4) &=x(3 x)+x(4)-2(4) \\ &=3 x^{2}+4 x-8 \end{aligned} </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (2k + 3)^2 -k(k+ 2)(k -2) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle 3(2 t+1)^{2}+2(3 t-1)(3 t+1) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle 3(a-2 b)^{2}-4(2 a+b)^{2} </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle \left(x^{2}+y^{2}\right)\left(x^{2}-y^{2}\right) </code></p>
<p>Simplify <code class='latex inline'>\displaystyle 2(b-a)+5(b-a) </code> and justify each step in your simplification.</p>
<p>Expand and simplify.</p><p><code class='latex inline'>(a+6)(a+6)</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(6z-5)^2</code></p>
<p>Expand the following.</p><p><code class='latex inline'>\displaystyle 4(x-9)(x+5) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle 5(x + 3) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(x+2)(x+1)</code></p>
<p>Use the Distributive Property to rewrite each expression. Then evaluate. <code class='latex inline'>\displaystyle 4(7-2) </code></p>
<p>Use the Distributive Property to rewrite each expression. Then evaluate. <code class='latex inline'>\displaystyle 6(6-1) </code></p>
<p>Simplify. <code class='latex inline'>\displaystyle -2(5 m+6) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (3x -4y)(5x + 2y) </code></p>
<p>Draw a diagram to illustrate the product.</p><p><code class='latex inline'> \displaystyle (a + 2)^2 </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle 2(m+3)(m+5)+4(2 m+3) </code></p>
<p>Expand and simplify.</p><p>a) <code class='latex inline'>\displaystyle -3(2m - 6) - (8 - 6m) </code></p><p>b) <code class='latex inline'>\displaystyle 4(2d-5) + 3(d^2 -3d) -2d(d+ 1) </code></p>
<p>Determine the missing terms.</p><p><code class='latex inline'>(x-5)(x-2)=x^2-\square-\circ+10</code></p>
<p>Find the product.</p><p><code class='latex inline'>\displaystyle (3 x-2)(2 x-1) </code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle -x(2 x-7) </code></p>
<p>Expand.</p><p><code class='latex inline'>\displaystyle (5 a+3 b)(5 a-3 b) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (w -8)^2 </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle \left(x^{2}+1\right)\left(x^{2}-1\right) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (2 x-3)(x+5)+(3 x+4)(4 x+1) </code></p>
<p>Find the product.</p><p><code class='latex inline'>\displaystyle (y-9)(y-9) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(2x-y)(3x+y)</code></p>
<p>Expand. Verify the solution by substituting 1 for the variable.</p><p><code class='latex inline'>\displaystyle (x-3)(x+3) </code></p>
<p>Expand and simplify. The first part has been done for you.</p><p><code class='latex inline'>\displaystyle 3(x+2) </code></p>
<p>Expand. Verify the solution by substituting 1 for the variable.</p><p><code class='latex inline'>\displaystyle (y+6)(y-2) </code></p>
<p>Determine the missing terms.</p><p><code class='latex inline'>(5m-2)(m-3)=5m^2-\square-2m+\circ</code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle 4\left(2 y^{2}+3 y-1\right) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (d-4)(d-2) </code></p>
<p>Use the Distributive Property to rewrite each expression. Then evaluate. <code class='latex inline'>\displaystyle (3+8) 15 </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (4 a-b)(2 a-5 b) </code></p>
<p>Expand the following.</p><p><code class='latex inline'>\displaystyle 0.5(x-1)(x+3) </code></p>
<p>Expand and simplify</p><p><code class='latex inline'>\displaystyle\begin{array}{c}-5(2 n-5)^{2}\end{array}</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle 2 a\left(a^{2}-2 a-1\right)-3 a\left(2 a^{2}+a-2\right) </code></p>
<p>Expand. Verify the solution by substituting 1 for the variable.</p><p><code class='latex inline'>\displaystyle (b-8)(b+8) </code></p>
<p>Expand and Simplify.</p><p><code class='latex inline'>\displaystyle (2 x-1)(x-4)-(3 x+2)(3 x-1) </code></p>
<p>Expand. Verify the solution by substituting 1 for the variable.</p><p><code class='latex inline'>\displaystyle (b-7)(b+10) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle \left(x^{2}+y^{2}\right)^{2} </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle 3(2a + 3b)(3a -2b) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>4(3a+2b)+3(2a-3b)-(a+2b)</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>6x(x+1)^2</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (x-6)^{2}-(x+5)(x-5) </code></p>
<p>Expand and simplify</p><p><code class='latex inline'>\displaystyle\begin{array}{c}-9(4 a-5)(4 a+5)\end{array}</code></p>
<p>Multiply each of the following,</p><p><code class='latex inline'>\displaystyle (10+2)(10-2) </code></p>
<p>Expand and simplify. </p><p><code class='latex inline'>\displaystyle 4\left(1+x^{2}\right)-3\left(x^{2}-3 x-2\right) </code></p>
<p>Simplify. <code class='latex inline'>\displaystyle 4(2 k-9) </code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle (2 x+3)(2 x-3) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (x+ 4)^2 </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(x-5)(x-3)</code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle -3 m(m-6) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(4x-1)(4x+1)-(x+3)^2</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'> \displaystyle (x + 6)(x - 6) </code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle -\left(4 m^{2}-m-7\right) </code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle 3 x(x+2) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (3 m+2)(m-3)-(2 m-1)(m+3) </code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle (5 x-1)^{2} </code></p>
<p>Expand and simplify each expression.</p><p> <code class='latex inline'>(4x+2y)^3</code></p>
<p>Expand each expression.</p><p><code class='latex inline'> \displaystyle (a + b)^2 </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle 4(1 -3k)-(2 -4k) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(m-9)(m+9)</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (x - 7)^2 </code></p>
<p>Expand.</p><p><code class='latex inline'>\displaystyle (y-4)(y+4) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle 2(3 x+1)(x+2)-3(4 x-5) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>2n(n+3)-3n(5-2n)+7n(1-4n)</code></p>
<p>Expand and simplify. Use a CAS to verify your answers.</p><p><code class='latex inline'>(3x^2+4x+2)^2</code></p>
<p>Multiply each of the following,</p><p><code class='latex inline'>\displaystyle (15+3)(15-3) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (x+4)^{2}+(x-2)^{2} </code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle 4(2 a+3 b-2 c) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'> \displaystyle (a - 7)(a + 7) </code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle (y+6)(y-6) </code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle 2(x-5) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (4 s-3 t)(5 s-6 t) </code></p>
<p>Expand and simplify</p><p><code class='latex inline'>3(x-6)(x+5)</code></p>
<p>Find the product.</p><p><code class='latex inline'>\displaystyle (c+2)(c-8) </code></p>
<p>Expand and Simplify.</p><p><code class='latex inline'>\displaystyle 2(x+1)(x-3) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(6x -2)(5x + 7)</code></p>
<p>Expand and simplify.</p><p> <code class='latex inline'>2(x-3)^2-(4x+1)(4x-1)</code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle (a-8 b)^{2} </code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle (4 m-5 n)(4 m+5 n) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (y-3)(y-1)-(y+2)(y-6) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (3x -3)(5x + 2) </code></p>
<p>ERROR ANALYSIS In Exercises 19 and 20 , describe and correct the error in finding the product of the binomials.</p><img src="/qimages/46065" /><p><code class='latex inline'>\displaystyle (x-5)(3 x+1) </code></p><p><code class='latex inline'>\displaystyle 3 x </code></p><p><code class='latex inline'>\displaystyle x </code></p><p><code class='latex inline'>\displaystyle 3 x^{2} </code> &amp; 1</p><p><code class='latex inline'>\displaystyle 15 x </code> &amp; <code class='latex inline'>\displaystyle x </code></p><p> <code class='latex inline'>\displaystyle (x-5)(3 x+1)=3 x^{2}+16 x+5 </code></p>
<p>Determine the missing terms.</p><p><code class='latex inline'>(r+4)(r-3)=r^2-3r+\square-\circ</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle 12-2(3 y+1)^{2}-(y-9)(3 y+2) </code></p>
<p>Expand and simplify. Verify your answers. Check that graphing both the original expression and the simplified expansion using a graphing calculator yields only one graph.</p><p><code class='latex inline'>(x-4)^2</code></p>
<p>Factor.</p><p><code class='latex inline'> \displaystyle 5x(2 -x)+4x(2x -5)-(3x -4) </code></p>
<p>Expand and simplify each expression.</p><p><code class='latex inline'>(2x-2)^3</code></p>
<p>Expand.</p><p><code class='latex inline'>\displaystyle (1-2 x)^{2} </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle \left(2 x^{2}+3\right)^{2} </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'> \displaystyle -2(5x + 7y)(5x - 7y) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle 4(3y + 2) +3 (2y - 7) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(7x-5)(x-3)</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle \left(4-3 c^{2}\right)\left(4+3 c^{2}\right) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (x+6)(x+4)+(x+2)(x+3) </code></p>
<p>Expand the following.</p><p><code class='latex inline'>\displaystyle 3(2 x-1)(3 x-2) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle 3(x-4)(x+3)-2(4 x-1) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (3 x-4)(3 x-4) </code></p>
<p>Use the Distributive Property to rewrite each expression. Then simplify.</p><p><code class='latex inline'>\displaystyle -3(2 x-6) </code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle (t-8)(t+8) </code></p>
<p>Expand each expression.</p><p><code class='latex inline'> \displaystyle (a + b)^1 </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle 2(2x + 2y)(3x - 2y) - 3(3x - y)^2 </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle 2(3 m-n)^{2}-3(2 m-5)(m+3) </code></p>
<p>Expand and simplify.</p><p> <code class='latex inline'>4(x-6)(x+7)</code></p>
<p>Draw a diagram to illustrate the product.</p><p><code class='latex inline'> \displaystyle (x + 4)^2 </code></p>
<p>A Pythagorean triple is a triple of natural numbers <code class='latex inline'>a, b, c</code> that satisfies the Pythagorean theorem <code class='latex inline'>a^2+b^2=c^2</code>, or equivalently, <code class='latex inline'>a^2=c^2-b^2</code>. For example, <code class='latex inline'>3,4,5</code> is a Pythagorean triple, since <code class='latex inline'>3^2+4^2=5^2</code>, or <code class='latex inline'>3^2=5^2-4^2</code>.</p><p>Show that <code class='latex inline'>(n+1)^2-n^2=2n+1</code></p>
<p>Use the Distributive Property to rewrite each expression. Then simplify.</p><p><code class='latex inline'>\displaystyle (5+n) 3 </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle 3 t^{2}-(3-2 t)^{2}+5(2 t-1)(2 t+1) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle 2(a+3)(a-3)+3(a+2)^{2} </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(x+2)(4x+1)</code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle -a(3 a+4 b-2 c) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(a+7)(a-9)</code></p>
<ol> <li>Use <code class='latex inline'>\displaystyle x=y-2 </code> to write each of the following in terms of <code class='latex inline'>\displaystyle y </code>. Then, expand and simplify.</li> </ol> <p><code class='latex inline'>\displaystyle x^{2}-2 x+3 </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(x+7)(x-3)</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (m-3)(m+3)+(m-4)^{2} </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle 2(3 x+2)(3 x+2)-3(2 x-1)(2 x-1) </code></p>
<p>Simplify each expression. If not possible, write simplified.</p><p><code class='latex inline'>\displaystyle 11(4 d+6) </code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle (y+6 x)(y-6 x) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle \left(x^{2}-y^{2}\right)^{2} </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(x+2)(x-3)</code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle -2 y\left(y^{2}+y-3\right) </code></p>
<p>Find the product.</p><p><code class='latex inline'>\displaystyle (q-2)(q+5) </code></p>
<p>Expand.</p><p><code class='latex inline'>2m(3m+4)</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (4c + 5d)^2 </code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle 2 x(3 x-4) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (n+ 3)(n -3) </code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle -3\left(x^{2}-2 x-1\right) </code></p>
<p>Simplify. <code class='latex inline'>\displaystyle 3(6 x+1) </code></p>
<ol> <li>Use <code class='latex inline'>\displaystyle x=y-2 </code> to write each of the following in terms of <code class='latex inline'>\displaystyle y </code>. Then, expand and simplify.</li> </ol> <p><code class='latex inline'>\displaystyle 3 x^{2}+5 x-9 </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'> \displaystyle (y + 12)(y - 12) </code></p>
<p>Expand and simplify. </p><p><code class='latex inline'>\displaystyle 5 x(x-3)-2 x(x+2) </code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle 7\left(9 y^{2}-3 y-7\right) </code></p>
<p>Use the Distributive Property to rewrite each expression. Then evaluate. <code class='latex inline'>\displaystyle 7(13+12) </code></p>
<p>Which pairs of functions are equivalent?</p><p><code class='latex inline'>h(t) = (4 -t)^3</code> and <code class='latex inline'>c(t) =(t -4)^3</code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle (x-3)(-4 x) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (5 y-7)(y+3) </code></p>
<p>Expand and simplify.</p><p> <code class='latex inline'>(9x-7y)^2</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (y+6)(y-6)+(y+7)^{2} </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle 5(2t - 5z)^2 + 3(4t-3z)(4t + 3z) </code></p>
<p>Expand.</p><p><code class='latex inline'>\displaystyle (x+4)^{2} </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle 3y(y^2 - y -1)-y(2y^2 - 3y + 4) </code></p>
<p>Expand each expression.</p><p><code class='latex inline'> \displaystyle (a + b)^3 </code></p>
<p>What two binomials are being multiplied and what is the product?</p><p><code class='latex inline'>\displaystyle \begin{array}{|c|c|c|r|r|r|}\hline x & x & x & -1 & -1 & -1 \\ \hline x & x & x & -1 & -1 & -1 \\ \hline x & x & x & -1 & -1 & -1 \\ \hline x & x & x & -1 & -1 & -1 \\ \hline x & x & x & -1 & -1 & -1 \\ \hline x^{2} & x^{2} & x^{2} & -x & -x & -x \\ \hline x^{2} & x^{2} & x^{2} & -x & -x & -x \\ \hline\end{array} </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(x - 2)(x - 5)</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (x-7)(x+5)-2(x+6)^{2} </code></p>
<p>Expand and simplify. </p><p><code class='latex inline'>\displaystyle 2(x+1)+3(x-1) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (x - 5)^2 </code></p>
<p>Simplify</p><p><code class='latex inline'>\displaystyle -3[9 - 2(k + 3)+ 5k] </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'> \displaystyle (y + 4x)^2 </code></p>
<p>Expand and Simplify.</p><p><code class='latex inline'>\displaystyle 3(2 x+1)(2 x-3) </code></p>
<p>Use the Distributive Property to rewrite each expression. Then evaluate. <code class='latex inline'>\displaystyle 14(8-5) </code></p>
<p>Which pairs of functions are equivalent?</p><p><code class='latex inline'>h(x) = (x + 6)(x + 3)(x-6)</code> and <code class='latex inline'>b(x) = (x + 3)(x^2 -36)</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (m -3)(m +3) + (m -4)^2 </code></p>
<p>Expand and Simplify.</p><p><code class='latex inline'>\displaystyle 4(m-2)(3 m-1) </code></p>
<p>Find the product.</p><p><code class='latex inline'>\displaystyle (y-3)(y+5) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>5(3x+2)^2</code></p>
<p>What binomial product does each diagram illustrate?</p><img src="/qimages/6058" />
<p>Expand and simplify.</p><p><code class='latex inline'>4x(2x+1)(x-3)-2x(x+4)(x-5)</code></p>
<p>Is <code class='latex inline'>x^2-1</code> the same as <code class='latex inline'>(x-1)^2</code>. Explain using words and/or diagrams.</p>
<p>Expand the following.</p><p><code class='latex inline'>\displaystyle 1.8(x+1)(x+1) </code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle (2 x+3 y)^{2} </code></p>
<p>Expand the following.</p><p><code class='latex inline'>\displaystyle -(a+3)(a-2) </code></p>
<p>Find the product.</p><p><code class='latex inline'>\displaystyle (a-4)(a-2) </code></p>
<p>Expand.</p><p>a) <code class='latex inline'>\displaystyle 3(y - 7) </code></p><p>b) <code class='latex inline'>\displaystyle -2(x + 3) </code></p><p>c) <code class='latex inline'>\displaystyle m(5m -3) </code></p><p>d) <code class='latex inline'>\displaystyle -4k(2k + 6) </code></p>
<p>Expand the following.</p><p><code class='latex inline'>\displaystyle 2(x+3)(x+5) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle 5(y-4)(3y + 1) + (3y -4)^2 </code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle 3 a(4 a-3 b) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (7 a+8 b)(a-b) </code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle -4 t(5 s-t) </code></p>
<p>If <code class='latex inline'>a^2+b^2=15</code> and <code class='latex inline'>ab=3</code>, then the value of <code class='latex inline'>(a-b)^2</code> is </p><p><strong>A.</strong> 21 </p><p><strong>B.</strong> 18</p><p><strong>C.</strong> 12</p><p><strong>D.</strong> 19</p><p><strong>E.</strong> 3</p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle -4\left(3 t^{2}-t-1\right) </code></p>
<p>Expand the following.</p><p><code class='latex inline'>\displaystyle 10(x+7)(x-5) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (x+5)(2 x+1) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle \left(8 a^{2}+3\right)\left(8 a^{2}-3\right) </code></p>
<p>Expand and simplify. </p><p><code class='latex inline'>\displaystyle 3\left(m^{2}+m+1\right)+2\left(m^{2}-1\right) </code></p>
<p>Use the Distributive Property to rewrite each expression. Then evaluate. <code class='latex inline'>\displaystyle (9-4) 19 </code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle (3 c+7 d)^{2} </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (2 x-3)^{2}-(3 x-1)(4 x+5) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'> \displaystyle 2x (4x - y)(4x + y) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (a-3)(2 a-5) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (3t -5)(3t + 5) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (2t + 1)^2 + 2(3t-1)(3t + 1) </code></p>
<p>Determine the missing terms.</p><p><code class='latex inline'>(2n+1)(3n-2)=\square-\circ+3n-2</code></p>
<p>Determine the missing terms.</p><p><code class='latex inline'>(m+3)(m+2)= \square + 2m + 3m + \bigcirc</code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle (x+5)^{2} </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle 5(3 t-1)^{2}-4(4 t-5)(4 t+5) </code></p>
<p>Simplify each expression.</p><p><code class='latex inline'>\displaystyle 6(6 a+5 b)-3(4 a+7 b) </code></p>
<p>Expand.</p><p><code class='latex inline'>-4g(2g-3)</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>-(x+3)(4x-1)</code></p>
<p>Expand and simplify</p><p> <code class='latex inline'>-2n(2n+1)+(n+2)^2</code></p>
<p>Find the product.</p><p><code class='latex inline'>\displaystyle (a+4)(a+4) </code></p>
<p>Expand and simplify. Use a CAS to verify your answers.</p><p><code class='latex inline'>(2x+1)(x+4)(3x+2)</code></p>
<p>Expand. Verify the solution by substituting 1 for the variable.</p><p><code class='latex inline'>\displaystyle (c+3)(c-4) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(5x+2)(x+2)</code></p>
<p>Expand. </p><p><code class='latex inline'>\displaystyle (x+3)(x-3) </code></p>
<p>Determine if the functions in each pair are equivalent.</p><p><code class='latex inline'>f(x) = -4(x^2 + x - 2) + (2x - 3)^2</code>, <code class='latex inline'>g(x) = x^2 - 16x + 17</code></p>
<p>Expand. Verify the solution by substituting 1 for the variable.</p><p><code class='latex inline'>\displaystyle (y-12)(y+3) </code></p>
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