College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter P, Prerequisites - Section P.6 - Factoring - P.6 Exercises: 46

Answer

$(2r-4t^2)(4r^2+8rt^2+16t^4)$

Work Step by Step

RECALL: $A^3-B^3=(A+B)(A^2+AB+B^2)$ The given binomial can be written as: $=2^3r^3-4^3(t^2)^3 \\=(2r)^3-(4t^2)^3$ The binomial above is a difference of two cubes. Factor using the the formula above with $A=2r$ and $B=4t^2$ to obtain: $=(2r-4t^2)[(2r)^2+(2r)(4t^2) +(4t^2)^2] \\=(2r-4t^2)(4r^2+8rt^2+16t^4)$
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