Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 5 - Section 5.6 - A General Factoring Strategy - Exercise Set - Page 378: 35

Answer

$(x+6-2a)(x+6+2a)$

Work Step by Step

The product of a binomial sum and a binomial difference is: $(A+B)(A-B)=A^2-B^2$. The square of a binomial sum is: $(A+B)^2=A^2+2AB+B^2$. The square of a binomial difference is: $(A-B)^2=A^2-2AB+B^2$. Hence here: $x^2-4a^2+12x+36=\\x^2+2\cdot x\cdot6+6^2-(2a)^2\\=(x+6)^2-(2a)^2\\=(x+6-2a)(x+6+2a)$
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