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 480: 59


$$4y^2(y - 3)(y + 3)$$

Work Step by Step

To factor this polynomial, we need to factor out the greatest common factor of both the coefficient and the variable: The greatest common factor of the coefficients $4$ and $36$ is $4$. The greatest common factor of the variables $y^4$ and $y^2$ is $y^2$. Therefore, we will factor out $4y^2$ from each term to get: $$4y^2(y^2 - 9)$$ We see that we now have a polynomial that is the difference of two squares, so we can further factor this polynomial. The formula for factoring the difference of two squares is given as: $$A^2 - B^2 = (A + B)(A - B)$$ We now plug in the values for $A$, which is the $\sqrt y^2$ or $y$, and $B$, which is the $\sqrt 9$ or $3$, to get: $$4y^2(y - 3)(y + 3)$$
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