How do you factor #a^3*b^6 - b^3#?

1 Answer
May 20, 2016

Answer:

#a^3*b^6-b^3=b^3*(a*b-1)(1+a*b+a^2*b^2)#

Explanation:

First, #a^3*b^6-b^3=(a^3*b^3-1)*b^3#.
Now there is a polynomial identity that can help us and which is
#(x^{n+1}-1)/(x-1)=1+x+x^2+x^3+...+x^n#
then
#a^3*b^3-1=(a*b-1)(1+a*b+a^2*b^2)#. Finally
#a^3*b^6-b^3=b^3*(a*b-1)(1+a*b+a^2*b^2)#