College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter R - Section R.4 - Factoring Polynomials - R.4 Exercises: 65

Answer

(3$y^{3}$ + 5$z^{2}$)($9y^{6}$ - 15$y^{3}z^{2}$ + 25$z^{4}$)

Work Step by Step

27$y^{9}$ + 125$z^{6}$ is a sum of cubes, so we write it as a sum of cubes and factor: $(3y^{3})^{3}$ + $(5z^{2})^{3}$ = (3$y^{3}$ + 5$z^{2}$)($(3y^{3})^{2}$ - 3$y^{3}(5z^{2}$) + $(5z^{2})^{2}$) = (3$y^{3}$ + 5$z^{2}$)($9y^{6}$ - 15$y^{3}z^{2}$ + 25$z^{4}$)
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