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 - Cumulative Review Exercises - Page 481: 18

Answer

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

Work Step by Step

Looking at this binomial, we see that we can first factor out a $y$ from each of the terms: $$y(y^4 - 16)$$ We see that the binomial within the parentheses can be factored as the product of two squares 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 case, $A$ is the $\sqrt(y^4)$, or $y^2$ and $B$ is the $\sqrt(16)$ or $4$. Let us plug these values into the formula: $$y(y^2 - 4)(y^2 + 4)$$ We can factor the $y^2 - 4$ term even further because it is also a difference of two squares. Here, the $A$ term is $\sqrt y^2$ or $y$ and $B$ is the $\sqrt 4$ or $2$. We use these values to plug into the equation for the difference of two squares: $$y(y - 2)(y + 2)(y^2 + 4)$$
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