College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter P, Prerequisites - Section P.5 - Algebraic Expressions - P.5 Exercises - Page 36: 87


The equations hold. See below for proof.

Work Step by Step

(a) We start with the right side: $\displaystyle \frac{1}{2}[(a+b)^{2}-(a^{2}+b^{2})]=\frac{1}{2}[(a^{2}+b^{2}+2ab)-a^{2}+b^{2}]=\frac{1}{2}(2ab)=ab$ Which equals the left side. (b) We start with the left side: $(a^{2}+b^{2})^{2}-(a^{2}-b^{2})^{2}=(a^{2})^{2}+(b^{2})^{2}+2a^{2}b^{2}-[(a^{2})^{2}+(b^{2})^{2}-2a^{2}b^{2}]=4a^{2}b^{2}$ Which equals the right side.
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