Factorization of a^7 + ab^6

a^7 + ab^6 = a (a^6 + b^6) , using distributive law

= a [ (a^2) ^ 3 + (b^2) ^ 3) ], using A^(M*N) = (A^M) ^ N

=a [ (a^2 + b^2) (a^4 - a^2 b^2 + b^4) ], using A^3 + B^3 = (A+B) ( A^2 -AB + B^2)

= a (a^2 + b^2) (a^4 - a^2 b^2 + b^4) Ans.