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Question 32438: Please help answer the following problem.
(x+1)^3 - (x-1)^3
This is what we have so far: (x+1)(x+1)(x+1) = x^3+3x^2+3x+1
However, we are confused about how to handle the subtration between the two expressions in parenthesis that needs to be cubed. Please provide a detailed description, because we have several problems with this same format.
Thanks so much!!
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! Please help answer the following problem.
(x+1)^3 - (x-1)^3
This is what we have so far: (x+1)(x+1)(x+1) = x^3+3x^2+3x+1
However, we are confused about how to handle the subtration between the two expressions in parenthesis that needs to be cubed. Please provide a detailed description, because we have several problems with this same format.
USE THE FORMULA
A^3-B^3=(A-B)(A^2+AB+B^2).....YOU CAN MULTIPLY AND CHECK...SO WE GET....
TAKING A=X+1 AND B=X-1,WE GET
(x+1)^3 - (x-1)^3={(X+1)-(X-1))*{(X+1)^2+(X+1)(X-1)+(X-1)^2}=
=(X+1-X+1)(X^2+1+2X+X^2-1+X^2+1-2X)
=2(3X^2-1)...IS THE ANSWER.
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