Question

How do i show that

(a-b)^2(a+b)+ab(a+b)=a^3+b^3
I have come up with the last part
ab(a+b)=a^2+b^2, but how do i work out the 1st part??

Answer 1

(a-b)^2(a+b)+ab(a+b)

multiply and combine like terms:
First multiply--shown in two steps...
=(a^2 - 2ab + b^2)(a + b) + (a^2)b + a(b^2)
=a^3 - 2(a^2)b + a(b^2) + (a^2)b - 2a(b^2) + b^3 + (a^2)b + a(b^2)

Now combine terms.