Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 7 - Cumulative Review Exercises - Page 565: 15


$$3(x - 5)(x + 5)$$

Work Step by Step

Looking at this expression, we can see that a $3$ can be factored out from each term: $$3(x^2 - 25)$$ After the $3$ was factored out, we have the difference of two squares left. We can factor this binomial according to the following formula: $$A^2 - B^2 = (A - B)(A + B)$$ where $A$ is the square root of the first term and $B$ is the square root of the second term. In this problem, $A$ is the $\sqrt x^2$ or $x$ and $B$ is the $\sqrt 25$ or $5$. We can plug these values into the formula: $$3(x - 5)(x + 5)$$
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