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: 58



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 and $(a\pm b)^2=a^2\pm2ab+b^2$ or the square of a binomial, the product of the given expression, $ (t+4)(t+4)(t-4)(t-4) ,$ is \begin{array}{l}\require{cancel} (t+4)^2(t-4)^2 \\\\= [(t+4)(t-4)]^2 \\\\= [(t)^2-(4)^2]^2 \\\\= (t^2-16)^2 \\\\= (t^2)^2-2(t^2)(16)+(16)^2 \\\\= t^4-32t^2+256 .\end{array}
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