SOLUTION: Please Help-I'm not sure how to factor this: 4(a-b)^2+7(a+b)

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The rules of precedence require you to first do the exponentiation, so you must first solve (a-b)^2.
Using the distributive property, (a-b)*(a-b) = a^2 - 2ab + b^2.
Then you substitute into your original equation:
4(a^2 - 2ab + b^2) + 7(a + b).
That gives you 4a^2 - 8ab + 4b^2 + 7a + 7b.