SOLUTION: My question is about factoring. If factoring is not considered an operation on exponents, sorry. There is no category for factoring. But I have a quiz tomorrow on factoring when ei

Algebra ->  Exponents -> SOLUTION: My question is about factoring. If factoring is not considered an operation on exponents, sorry. There is no category for factoring. But I have a quiz tomorrow on factoring when ei      Log On


   

Question 537823: My question is about factoring. If factoring is not considered an operation on exponents, sorry. There is no category for factoring. But I have a quiz tomorrow on factoring when either square is a square of a polynomial.
This is the example in my textbook: +25a%5E2-%283a%2B2b%29%5E2+ . Somehow that's supposed to come out to 4(4a+b)(a-b) . I'm a little confused, the book doesn't explain it very well, and I would greatly appreciate your help. Thank you.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
+25a%5E2-%283a%2B2b%29%5E2+
FOIL (3a+2b)(3a+2b) to 9a^2 + 12ab + 4b^2, then you have
+25a%5E2-%289a%5E2+%2B+12ab+%2B+4b%5E2%29+
Remove the brackets, this changes the signs
+25a%5E2+-+9a%5E2+-+12ab+-+4b%5E2%29+
Combine the like terms
+16a%5E2+-+12ab+-+4b%5E2%29+
Factor out 4
+4%284a%5E2+-+3ab+-+b%5E2%29+
Factor again
+4%284a%2Bb%29%28a-b%29+
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