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 5.5 - Factoring Special Forms - Exercise Set - Page 372: 67

Answer

$(x+10-x^2)(x+10+x^2)$

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: $x^2+20x+100-x^4=\\=x^2+2\cdot10\cdot x+10^2-(x^2)^2=\\=(x+10)^2-(x^2)^2\\=(x+10-x^2)(x+10+x^2)$
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