Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 4 - Polynomials - 4.7 Polynomials in Several Variables - 4.7 Exercise Set: 70

Answer

$a^2-b^2-2bc-c^2$

Work Step by Step

Using grouping symbols, the given expression, $ (a+b+c)(a-b-c) ,$ is equivalent to \begin{array}{l}\require{cancel} [a+(b+c)][a-(b+c)] .\end{array} Using $(a+b)(a-b)=a^2-b^2$ or the product of the sum and difference of like terms, the expression above simplifies to \begin{array}{l}\require{cancel} (a)^2-(b+c)^2 \\\\= a^2-(b+c)^2 .\end{array} Using $(a+b)^2=a^2+2ab+b^2$ or the square of a binomial, the expression above simplifies to \begin{array}{l}\require{cancel} a^2-[(b)^2+2(b)(c)+(c)^2] \\\\= a^2-[b^2+2bc+c^2] \\\\= a^2-b^2-2bc-c^2 .\end{array}
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