How do you factor completely #x^2(a^2+2ab+b^2) = x(a+b)#?

1 Answer
Jun 16, 2015

Answer:

You can first factor #(a^2+2ab+b^2)=(a+b)^2#

Explanation:

The left part can then be rewritten:
#x^2*(a+b)^2=[x(a+b)]^2#
The complete equation changes into:
#[x(a+b)]^2=x(a+b)#

This is of the form #Q^2=Q# and there are only two solutions:
#Q=0orQ=1#

For #Q=0->x=0or(a+b)=0->a=-b#

For #Q=1->x*(a+b)=1->x=1/(a+b)#