Introductory Algebra for College Students (7th Edition)

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

Chapter 6 - Review Exercises - Page 479: 34


$$2x(3y + 2)(3y - 2)$$

Work Step by Step

We see from the binomial that we can factor out an $2x$ from both terms to simplify it: $$2x(9y^2 - 4)$$ We see now that we have the difference of two squares, so we use the following formula: $$A^2 - B^2 = (A + B)(A - B)$$ For this binomial, we take the square root of the leading term $(9y^2)$ to get $A = 3y$ and the square root of the second term $(41)$ to get $B = 2$. So we now plug these two values into the formula for factoring the binomial: $$2x(3y + 2)(3y - 2)$$
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