SOLUTION: Fully factor 81(7a+3)^4 - 72(7a+3)^2 + 16 I would like MathTherapy to solve my question please!!

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Question 1134228: Fully factor 81(7a+3)^4 - 72(7a+3)^2 + 16
I would like MathTherapy to solve my question please!!
Found 2 solutions by Alan3354, greenestamps:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Make an effort.
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%28a+-+b%29%5E2+=+a%5E2+-+2ab+%2B+b%5E2
%283a+-+4b%29%5E2+=+9a%5E2+-+24ab+%2B+16b%5E2

Answer by greenestamps(13196) About Me  (Show Source):
You can put this solution on YOUR website!


When factoring complicated-looking expressions, it is a good idea to look first at some common patterns:

a^2+2ab+b^2 = (a+b)^2 [three terms; first and last terms positive perfect squares, middle term positive]

a^2-2ab+b^2 = (a-b)^2 [three terms; first and last terms positive perfect squares, middle term negative]

a^2-b^2 = (a+b)(a-b) [two terms; both perfect squares; first positive and second negative]

This example fits one of those patterns (first and last terms positive perfect squares; middle term negative):

81(7a+3)^4 = [9(7a+3)^2)]^2; 16 = 4^2