Question

factorize a^3+b^3+a+b

Answer 1

A^3+B^3 can be written as ...
A+B(A^2-AB+B^2)
So A^3+B^3+A+B= (A+B)(A^2-AB+B^2+1)

Answer 2

it can be as follow...
a^3+b^3 = (a+b)(a^2+b^2-ab)
now,
a^3 + b^3 + (a+b)=(a+b)(a^2+b^2-ab)(a+b)
taking (a+b) as common...
(a+b)(a^2+b^2-ab+1)