Use the distributive property to find the binomial product.
\displaystyle
(x + 5)(x + 8)
Use the distributive property to find the binomial product.
\displaystyle
(x - 1)(x -4)
Use the distributive property to find the binomial product.
\displaystyle
(x + 3y)(x -6y)
Use the distributive property to find the binomial product.
\displaystyle
(5a -6b)(2a + 9b)
Expand and simplify.
\displaystyle
-(k + 2)(k - 7)
Expand and simplify.
\displaystyle
w(w - 7v)(w- 3v)
Expand and simplify.
\displaystyle
7x(7x + 3y)(3x + 9y)
Expand and simplify.
\displaystyle
(y + 1)(y + 8)+ (y-8)(y + 1)
Expand and simplify.
\displaystyle
-4(2x -6)(4x -5)+3(11x + 7)( 11x - 4)
Write an algebraic expression to represent the area of the figure.
Expand and simplify.
Draw a diagram to illustrate the product.
\displaystyle
(x + 4)^2
Draw a diagram to illustrate the product.
\displaystyle
(a + 2)^2
Expand and simplify.
a)
\displaystyle
(x + 6)^2
b)
\displaystyle
(k+ 8)^2
c)
\displaystyle
(p + 7)^2
Expand and simplify.
i)
\displaystyle
(r- 2)^2
ii)
\displaystyle
(e- 9)^2
iii)
\displaystyle
(q- 20)^2
Expand and simplify.
\displaystyle
(b + 6)(b - 6)
Expand and simplify.
\displaystyle
(a - 7)(a + 7)
Expand and simplify.
\displaystyle
(y + 12)(y - 12)
Expand and simplify.
\displaystyle
(x - 15)(x + 15)
Expand and simplify.
\displaystyle
(e - 10)(e + 10)
Expand and simplify.
\displaystyle
(x + 6)(x - 6)
Expand and simplify.
\displaystyle
(y + 4x)^2
Expand and simplify.
\displaystyle
(7m - n)^2
Expand and simplify.
\displaystyle
(2c + 9d)^2
Expand and simplify.
\displaystyle
-2(5x + 7y)(5x - 7y)
Expand and simplify.
\displaystyle
(3a - 8c)(3a + 8c)
Expand and simplify.
\displaystyle
-(5x - 8y)(5x + 8y)
Use algebra tiles or a diagram to illustrate the factoring of each polynomial.
\displaystyle
x^2 + 9x
Use algebra tiles or a diagram to illustrate the factoring of each polynomial.
\displaystyle
3x^2 + x
Factor.
a)
\displaystyle
12y + 24z
b)
\displaystyle
11xy - 9xz
c)
\displaystyle
c^2 + 3c
d)
\displaystyle
4k - 8k^3
Factor by grouping.
\displaystyle
4m^2 + 12m + 3m + 9
Factor by grouping.
\displaystyle
9k^2 - 6k + 6k -4
Factor by grouping.
\displaystyle
8x^2 + 16x - 5x -10
Factor by grouping.
\displaystyle
16x^2 - 12xy - 12xy + 9y^2
Factor by grouping.
\displaystyle
8m^2 - 16m + 4
Factor by grouping.
\displaystyle
18c^3 + 24c^2 - 8c + 6
Factor by grouping.
\displaystyle
15m^2 - 22mn + 66mn^2
Factor by grouping.
\displaystyle
ax^2z - az^2 + axz
A rectangle has area given by the expression 10x^2 + 5x. The length and width can be
found by factoring the expression. Find all possible expressions for the length and width.
Illustrate the factoring of each trinomial using algebra tiles or a diagram.
\displaystyle
x^2 + 9x + 14
Illustrate the factoring of each trinomial using algebra tiles or a diagram.
\displaystyle
x^2 + 11x + 18
Illustrate the factoring of each trinomial using algebra tiles or a diagram.
\displaystyle
x^2 + 4x + 4
Factor.
\displaystyle
c^2 - 17c + 72
Factor.
\displaystyle
x^2 - 8x + 15
Factor.
\displaystyle
z^2- 14z + 33
Factor.
\displaystyle
x^2 + 3x - 10
Factor.
\displaystyle
x^2 + 8x -9
Factor.
\displaystyle
x^2 -2x -8
A parabola has equation y = x^2 -3x - 18.
a) Factor the right side of the equation.
b) Identify the x-intercepts of the parabola.
c) Find the equation of the axis of symmetry
Factor.
\displaystyle
2x^2 + 7x + 6
Factor.
\displaystyle
6y^2 + 29y + 9
Factor.
\displaystyle
6a^2 - 23a + 15
Factor.
\displaystyle
4b^2 - 5b + 1
Factor.
\displaystyle
12m^2 + 20m - 8
Factor.
\displaystyle
14k^2 -31k - 10
Factor.
\displaystyle
8x^2 + 2xy - 15y^2
Factor.
\displaystyle
5c^2 - 4cd+ 9d^2
Factor.
\displaystyle
12m^2 + 13mn + 3n^2
Factor.
\displaystyle
2w^2 - 9wx - 8x^2
Factor.
\displaystyle
24x^2 + 6xy - 9y^2
Factor.
\displaystyle
9g^2 + 4g - 10
A rectangle has area defined by 8x^2 + 2x - 15.
a) Factor to find algebraic expressions for the length and width of the rectangle.
b) If x represents 12 cm, determine the perimeter and the area of the rectangle.
Factor.
\displaystyle
x^2 - 49
Factor.
\displaystyle
y^2 - 121
Factor.
\displaystyle
4k^2 - 9
Factor.
\displaystyle
16 - 144a^2
Factor.
\displaystyle
9w^2 -25x^2
Factor.
\displaystyle
1 - 81p^2
Verify that the trinomial is a perfect square. Then, factor.
\displaystyle
x^2 + 14x + 49
Verify that the trinomial is a perfect square. Then, factor.
\displaystyle
k^2 + 8k + 16
Verify that the trinomial is a perfect square. Then, factor.
\displaystyle
y^2 - 10y + 25
Verify that the trinomial is a perfect square. Then, factor.
\displaystyle
25y^2 -70y + 49
Verify that the trinomial is a perfect square. Then, factor.
\displaystyle
36c^2 - 108c + 81
Verify that the trinomial is a perfect square. Then, factor.
\displaystyle
121 +176y + 64y^2
Determine all values of k so that each trinomial is a perfect square.
25y2 + ky + 144
Determine all values of k so that each trinomial is a perfect square.
9x^2 - 42x + k
Factor, if possible.
\displaystyle
9w^2x^2 - 24wxyz + 16y^2z^2
Factor, if possible.
\displaystyle
625 - (y -5)^2
Factor, if possible.
\displaystyle
144a^4 - 499b^4
Factor, if possible.
\displaystyle
25x^2 + 30x + 4