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: 88

Answer

The equation holds. See below for proof.

Work Step by Step

We start with the left side: $(a^{2}+b^{2})(c^{2}+d^{2})=a^{2}c^{2}+a^{2}d^{2}+b^{2}c^{2}+b^{2}d^{2} =(a^{2}c^{2}+b^{2}d^{2}+2abcd)+(a^{2}d^{2}+b^{2}c^{2}-2abcd)=(ac+bd)^{2}+(ad-bc)^{2}$ Which equals the right side.
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