Question

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

Answer 1

Answer:   (x-2)(x+2)(x+3)(x+3)

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

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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

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Side notes:

• Difference of squares rule is a^2 - b^2 = (a-b)(a+b)
• The perfect square trinomial factoring rule is a^2+2ab+b^2 = (a+b)^2