College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter R - Section R.3 - Polynomials - R.3 Exercises - Page 29: 69



Work Step by Step

Using $(a+b)(a-b)=a^2-b^2$ or the special product of the sum and difference of like terms, the product of the given expression, $ [(3q+5)-p][(3q+5)+p] ,$ is \begin{array}{l}\require{cancel} (3q+5)^2-(p)^2 \\\\= (3q+5)^2-p^2 .\end{array} Using $(a\pm b)^2=a^2\pm2ab+b^2$ or the square of a binomial, the expression, $ (3q+5)^2-p^2 ,$ is equivalent to \begin{array}{l}\require{cancel} (3q)+2(3q)(5)+(5)^2-p^2 \\\\= 9q^2+30q+25-p^2 .\end{array}
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