College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter P - Prerequisites: Fundamental Concepts of Algebra - Exercise Set P.4: 87

Answer

$16x^4-625$

Work Step by Step

$$(2x+5)(2x-5)(4x^2+25)$$ To multiply the sum of two terms by the difference of two terms, use the formula: $(a+b)(a-b)=a^2-b^2$: $$=[(2x)^2-(5)^2](4x^2+25)$$ $$=(4x^2-25)(4x^2+25)$$ This is also the product of the sum of two terms by the difference of two terms!: $$=(4x^2)^2-(25)^2$$ $$=16x^4-625$$
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