College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter P - Prerequisites: Fundamental Concepts of Algebra - Exercise Set P.5 - Page 75: 108



Work Step by Step

$(y+1)^{3} + 1$ To factor $(y+1)^{3} + 1$, Express each term as the cube of some monomial. $(y+1)^{3} + 1^{3}$ Then use the formula $A^{3} + B^{3} = ( A + B )(A^{2} -AB+B^{2})$ for factoring. $(y+1)^{3} + 1$ $= (y+1+1)[(y+1)^{2}-(y+1)(1)+1^{2}]$ $= (y+2) [(y+1)^{2}-(y+1)(1)+1^{2}]$ $= (y+2) [(y+1)^{2}-(y+1)+1]$ $= (y+2) [(y+1)^{2}-y-1+1]$ $= (y+2) [(y+1)^{2}-y]$ The square of the binomial can be found using the formula, $(a+b)^{2}=a^{2}+2ab+b^{2}$ $= (y+2) [(y)^{2}+2(y)(1)+1^{2}-y]$ $= (y+2) [y^{2}+2y+1-y]$ Combine like terms. $= (y+2) (y^{2}+y+1)$
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