How do you factor a^3*b^6 - b^3a3⋅b6−b3?

1 Answer
Cesareo R.
May 20, 2016

a^3*b^6-b^3=b^3*(a*b-1)(1+a*b+a^2*b^2)a3⋅b6−b3=b3⋅(a⋅b−1)(1+a⋅b+a2⋅b2)

Explanation:

First, a^3*b^6-b^3=(a^3*b^3-1)*b^3a3⋅b6−b3=(a3⋅b3−1)⋅b3.
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)

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