8. Q8a
Save videos to My Cheatsheet for later, for easy studying.
Video Solution
Q1
Q2
Q3
L1
L2
L3
Similar Question 1
<p>The two equal sides of an isosceles triangle each have a length of <code class='latex inline'>2x + 3y - 1</code>. The perimeter of the triangle is <code class='latex inline'>7x + 9y</code>. Determine the length of the third side.</p>
Similar Question 2
<p>Expand and simplify using tools and methods of your choice.</p><img src="/qimages/60408" />
Similar Question 3
<p>Simplify.</p><p><code class='latex inline'>(xy - xz + 4yz) + (2x - 3yz) - (4y - xz)</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.</p><p><code class='latex inline'>(4a^2-9)-(a^3+2a-9)</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle 2(x -4)(x - 7)-5(8x -9)(8x + 9) </code></p>
<p>Determine whether each pair of functions is equivalent.</p><p><code class='latex inline'>f(n) = 0.5n^2 + 2n - 3 + (1.5n^2 - 6)</code> and <code class='latex inline'>g(n) = n^2 - n + 1 - ( -n^2 - 3n + 10)</code></p>
<p>Kenny wrote a mathematics contest consisting of 25 multiple-choice questions. The scoring system gave 6 points for a correct answer, 2 points for not answering a question, and 1 point for an incorrect answer. Kenny got <code class='latex inline'>x</code> correct answers and left <code class='latex inline'>y</code> questions unanswered.</p><p><strong>(a)</strong> Write an expression for the number of questions he answered incorrectly.</p><p><strong>(b)</strong> Write an expression, in simplified form, for Kenny&#39;s score.</p><p><strong>(c)</strong> Use the expressions you wrote in parts (a) and (b) to determine Kenny&#39;s score if he answered 13 questions correctly and 7 incorrectly.</p>
<p>Simplify </p><p><code class='latex inline'>\displaystyle (x-3)(x+4)+3(x^2-x+2) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>-4(5r-3)(3r+2)+5(3r+4)(2r-5)</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>5(3y-4)(2y-3)-3(4y+1)(2y-1)</code></p>
<p>Simplify the following.</p><p> <code class='latex inline'>\displaystyle (3x + 5)(2x - 4) + (x + 1)(2x + 5) </code></p>
<p>Simplify.</p><p><code class='latex inline'>(2x^2 - 4x + 3) - (x^2 - 3x + 2) + (x^2 - 1)</code></p>
<p>Determine whether each pair of functions is equivalent.</p><p><code class='latex inline'>f(m) = m(5 - m) - 2(2m - m^2)</code> and <code class='latex inline'>g(m) = 4m^2(m - 1) - 3m^2 + 5m</code></p>
<p>Determine whether each pair of functions is equivalent.</p><p><code class='latex inline'>y_1 = 3p(q -2) + 2p(q + 5)</code> and <code class='latex inline'>y_2 = p(q + 4)</code></p>
<p>Determine whether each pair of functions is equivalent.</p><p><code class='latex inline'>y_1 = (x -1)(x)(x + 2)</code> and <code class='latex inline'>y_2 = 3x(x^2-1)</code></p>
<p>Expand and simplify using tools and methods of your choice.</p><img src="/qimages/60405" />
<p>Expand each pair of binomials, Compare the answers.</p><p><code class='latex inline'>(x-6)(x-9)</code> and <code class='latex inline'>(x-6y)(x-9y)</code></p>
<p>Simplify.</p><p><code class='latex inline'>(-4x^2 -2xy) + (6x^2-3xy+2y^2)</code></p>
<p>Simplify.</p><p><code class='latex inline'>(x^2 + y^2 + 8) + (4x^2 - 2y^2 - 9)</code></p>
<p>Expand and simplify using tools and methods of your choice.</p><img src="/qimages/60406" />
<p>Simplify.</p><p><code class='latex inline'>(3x^2 - 2x) + (x^2 - 7x) - (7x + 3)</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(c-4)(c+6)-(c+2)(c-3)</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (2x +5)(3x - 7)+2(4x + 9)(2x -11)</code></p>
<p>Simplify.</p><p><code class='latex inline'>(m - n + 2p)-(3n + p - 7)</code></p>
<p>Simplify.</p><p><code class='latex inline'>(2x -y)-(-3x + 4y)+(6x -2y)</code></p>
<p>Simplify.</p><p><code class='latex inline'>(3x^2-2x)-(x^2 -7x)+(7x + 3)</code></p>
<p>Expand and simplify.Expand and simplify.</p><p><code class='latex inline'>\displaystyle 3(6x-2)(6x -1)-(2x - 3)(5x + 6)</code></p>
<p>Simplify.</p><p><code class='latex inline'>(2a + 4c + 8) + (7a - 9c - 3)</code> </p>
<p>Simplify.</p><p><code class='latex inline'>(6x + 2y+ 9) + (-3x - 5y - 8)</code></p>
<p>Simplify.</p><p><code class='latex inline'>(xy - xz + 4yz) + (2x - 3yz) - (4y - xz)</code></p>
<p>Tony owns a small company that produces and sells cellphone cases. The revenue and cost functions for Tony&#39;s company are shown below, where <code class='latex inline'>x</code> represents the selling price in dollars. </p> <ul> <li><strong>Revenue</strong>: <code class='latex inline'>R(x) = -50x^2 + 2500x</code></li> <li><strong>Cost</strong> : <code class='latex inline'>C(x) = 150x + 9500</code></li> </ul> <p>(a) Write the simplified form of the profit function, <code class='latex inline'>P(x) = R(x) - C(x)</code>.</p><p>(b) What profit will the company make if it sells the cases for $12 each?</p>
<p>Expand and simplify using tools and methods of your choice.</p><img src="/qimages/60410" />
<p>Simplify.</p><p> <code class='latex inline'>(2x^2 - 7x + 6) + (x^2 - 2x - 9)</code></p>
<p>The two equal sides of an isosceles triangle each have a length of <code class='latex inline'>2x + 3y - 1</code>. The perimeter of the triangle is <code class='latex inline'>7x + 9y</code>. Determine the length of the third side.</p>
<p>Simplify.</p><p><code class='latex inline'>(x^2 - 6x + 1) - (-x^2 - 6x + 5)</code></p>
<p>Expand and simplify using tools and methods of your choice.</p><img src="/qimages/60408" />
<p>Expand and simplify.</p><p><code class='latex inline'> \displaystyle -4(2x -6)(4x -5)+3(11x + 7)( 11x - 4) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle -5(3x -1)(5x - 2)+6(6x +3)(5x -2)</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle -(x - 2)(x - 3)+2(3x + 5)(x + 4)</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (3n -2)^2 + (3n + 2)^2 </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(y+6)(y-3)+(y-5)(y+4)</code></p>
<p>Simplify.</p><p><code class='latex inline'>(3x + 4y - 5z) + (2x^2 + 6z)</code></p>
<p>Show that <code class='latex inline'>f(x)</code> and <code class='latex inline'>g(x)</code> are not equivalent by evaluating each function at a suitable value of x.</p> <ul> <li><code class='latex inline'>f(x) = 2(x - 3) + 3(x - 3)</code></li> <li><code class='latex inline'>g(x) = 5(2x - 6)</code></li> </ul>
<p>Show that <code class='latex inline'>f(x)</code> and <code class='latex inline'>g(x)</code> are equivalent by simplifying each.</p> <ul> <li><code class='latex inline'>f(x) = (2x - 1) - (3 - 4x) + (x + 2)</code></li> <li><code class='latex inline'>g(x) = (-x + 6) + (6x - 9) - (-2x - 1)</code></li> </ul>
<p>Expand and simplify.</p><p><code class='latex inline'>(g+6)^2-(g-6)^2</code></p>
<p>Simplify.</p><p><code class='latex inline'>(\frac{3}{4}x + \frac{1}{2}y) - (\frac{2}{3}x + \frac{1}{4}y - 1)</code></p>
<p>Simplify.</p><p><code class='latex inline'>(-6m - 2q + 8) + (2m + 2q + 7)</code></p>
<p> Expand the following. Before expanding, simplify the signs of the terms inside each brackets if possible.</p><p> <code class='latex inline'>\displaystyle (c - 2)( - 2c - 2) </code></p>
<p>Simplify.</p><p><code class='latex inline'>(\frac{1}{2}+ \frac{1}{3}y)-(\frac{1}{5}x -y)</code></p>
<p>Simplify.</p><p><code class='latex inline'>(3x^2+2y^2+7)-(4x^2-2y^2-8)</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle -2(3a +b)(3a - b) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle 2x(x -6) -3 (2x -5) </code></p>
<p>Expand and simplify using tools and methods of your choice.</p><img src="/qimages/60409" />
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (x + 4)^2 -(x -4)^2</code></p>
<p>Simplify </p><p><code class='latex inline'>\displaystyle (3x+5)(2x-4)+(x+1)(2x+5) </code></p>
<p> Expand and collect the like terms.</p><p><code class='latex inline'>\displaystyle (2x - 3)^2 - (2x - 3 )(2x +3) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>(x+3)(x+5)+(x+4)(x+2)</code></p>
<p>Simplify.</p><p><code class='latex inline'>(3x^2 - 7x + 5) + (x^2 - x + 3)</code></p>
<ul> <li>Expand the first expression and simply and</li> <li>Expand then simplify the first expression then factor both to show that </li> </ul> <p> <code class='latex inline'>(3x^2 - x) - (5x^2 - x)</code> <strong>and</strong> <code class='latex inline'>-2x^2 - 2x</code> are not equivalent. </p>
<p>Simplify.</p><p><code class='latex inline'>(2m^2 - 6mn + 8n^2) - (4m^2 - mn - 7n^2)</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'> \displaystyle (y + 1)(y + 8)+ (y-8)(y + 1) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>3(2x+3)(3x-5)+4(5x-2)(4x+3)</code></p>
<p>Expand and simplify using tools and methods of your choice.</p><img src="/qimages/60407" />
<p> Expand the following. Before expanding, simplify the signs of the terms inside each brackets if possible.</p><p> <code class='latex inline'>\displaystyle (-a - 2)(a - 2) </code></p>
<p>Ronson used his graphing calculator to graph three different polynomial functions on the same axes. The equations of the functions all appeared to be different, but his calculator showed only two different graphs. He concluded that two of his functions were equivalent.</p><p>(a) Is his conclusion correct? Explain.</p><p>(b) How could he determine which, if any, of the functions were equivalent without using his graphing calculator?</p>
<p>Expand and simplify.</p><p><code class='latex inline'>-(k+7)(k+5)+(k-6)(k-3)</code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle 3x(2x- 1)-4x(3x + 2) - (-x^2 +4x) </code></p>
<p>Expand and simplify.</p><p><code class='latex inline'>\displaystyle (x +4)(x + 6)+(x - 1)(x + 7)</code></p>
How did you do?
I failed
I think I failed
I think I got it
I got it
Another question?
Found an error or missing video? We'll update it within the hour! 👉
Report it
Save videos to My Cheatsheet for later, for easy studying.