Algebra 1: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281140
ISBN 13: 978-0-13328-114-9

Chapter 8 - Polynomials and Factoring - 8-7 Factoring Special Cases - Practice and Problem-Solving Exercises - Page 527: 39



Work Step by Step

Recognize that $x^{4}=(x^{2})^{2},$ and $y^{4}=(y^{2})^{2}.$ $x^{4}-y^{4}= $ ...write the difference as $a^{2}-b^{2}$. $(x^{2})^{2}-(y^{2})^{2} =$ ...factor using the rule for a difference of two squares. ($a^{2}-b^{2}=(a+b)(a-b),\quad a=x^{2},\ b=y^{2}$) $=(x^{2}+y^{2})(x^{2}-y^{2})$ ... the first parentheses is a sum of squares. There is no special formula for that. But, the second parentheses contain a difference of two squares... $=(x^{2}+y^{2})(x+y)(x-y)$
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