Question

Factor completely: 9x3 + 9x2y - 4x - 4y

Answer 1

Answer:

$(x+y)(3x+2)(3x-2)$

Step-by-step explanation:

The given expression is $9x^3+9x^2y-4x-4y$

Make group as shown below

$(9x^3+9x^2y)+(-4x-4y)$

Factor out GCF from each of the group

$9x^2(x+y)-4(x+y)$

Now, factored out the common term

$(x+y)(9x^2-4)$

Now, rewrite the expression in perfect square form

$(x+y)((3x)^2-2^2)$

Apply the difference of squares formula: $a^2-b^2=(a+b)(a-b)$

$(x+y)(3x+2)(3x-2)$

Hence, the factored form of the given expression is

$(x+y)(3x+2)(3x-2)$

Answer 2

$9x^3 + 9x^2y - 4x - 4y$

$= 9x^2(x + y) -4(x + y)$

$= (x +y)(9x^2-4)$

$= (x +y)(3x - 2)(3x + 2)$