Factor completely. (x^2 – 4)(x^2 + 6x + 9)

This is the same as (x-2)(x+2)(x+3)^2. The order of the factors doesn't matter.

Explanation:

x^2-4 factors to (x-2)(x+2) after using the difference of squares rule

x^2+6x+9 factors to (x+3)(x+3) after using the perfect square trinomial factoring rule

So overall, the original expression factors to (x-2)(x+2)(x+3)(x+3)

We can condense this into (x-2)(x+2)(x+3)^2 since (x+3)(x+3) is the same as (x+3)^2

Side notes:

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11