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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Step-by-step 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