How do you factor (a-b)^2 - 16(a+2b)^2(a−b)2−16(a+2b)2?

1 Answer
George C.
Sep 17, 2016

(a-b)^2-16(a+2b)^2 = -3(a+3b)(5a+7b)(a−b)2−16(a+2b)2=−3(a+3b)(5a+7b)

Explanation:

The difference of squares identity can be written:

A^2-B^2=(A-B)(A+B)A2−B2=(A−B)(A+B)

Let A=(a-b)A=(a−b) and B=4(a+2b)B=4(a+2b)

Then we find:

(a-b)^2-16(a+2b)^2 = (a-b)^2-(4(a+2b))^2(a−b)2−16(a+2b)2=(a−b)2−(4(a+2b))2

color(white)((a-b)^2-16(a+2b)^2) = ((a-b)-4(a+2b))((a-b)+4(a+2b))(a−b)2−16(a+2b)2=((a−b)−4(a+2b))((a−b)+4(a+2b))

color(white)((a-b)^2-16(a+2b)^2) = (a-b-4a-8b)(a-b+4a+8b)(a−b)2−16(a+2b)2=(a−b−4a−8b)(a−b+4a+8b)

color(white)((a-b)^2-16(a+2b)^2) = (-3a-9b)(5a+7b)(a−b)2−16(a+2b)2=(−3a−9b)(5a+7b)

color(white)((a-b)^2-16(a+2b)^2) = -3(a+3b)(5a+7b)(a−b)2−16(a+2b)2=−3(a+3b)(5a+7b)

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