SOLUTION: Factor completely: {{{(x+1)^3 * x - 2(x+1)^2 * x^2 + x^3(x+1)}}}

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Factor completely: {{{(x+1)^3 * x - 2(x+1)^2 * x^2 + x^3(x+1)}}}       Log On


   

Question 540953: Factor completely:
%28x%2B1%29%5E3+%2A+x+-+2%28x%2B1%29%5E2+%2A+x%5E2+%2B+x%5E3%28x%2B1%29

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
if we replace (x+1) with a, then we get:
a%5E3%2Ax+-+2a%5E2%2Ax%5E2+%2B+ax%5E3
we can factor out an x and an a to get:
ax%28a%5E2+-+2ax+%2B+x%5E2%29
we can factor a%5E2+-+2ax+%2B+x%5E2 to get:
ax%28a-x%29%5E2
we now replace a with (x+1) to get:
%28x%2B1%29%2Ax%2A%28%28x%2B1%29-x%29%5E2