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 R - Elementary Algebra Review - R.5 Polynomials and Factoring - R.5 Exercise Set: 4

Answer

$(2z+5)(2z-5)$

Work Step by Step

The expressions $ 4z^2 $ and $ 25 $ are both perfect squares (the square root is exact) and are separated by a minus sign. Hence, $ 4z^2-25 ,$ is a difference of $2$ squares. Using the factoring of the difference of $2$ squares which is given by $a^2-b^2=(a+b)(a-b),$ the expression above is equivalent to \begin{array}{l}\require{cancel} (2z)^2-(5)^2 \\\\= (2z+5)(2z-5) .\end{array}
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