Question

Pls explain this to me, I don't understand why the answer is a^3 +b^3 and not a^3-b^3

Answer 1

`(a+b)(a^2-ab+b^2)=a^3+b^3`

Explanation:

Given expression:

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

Using the Distributive Property Law, expand the brackets:

`\implies a(a^2-ab+b^2)+b(a^2-ab+b^2)`

`\implies a^3-a^2b+ab^2+a^2b-ab^2+b^3`

Group like terms:

`\implies a^3+b^3-a^2b+a^2b+ab^2-ab^2`

As -a²b+a²b=0 and ab²-ab²=0 then:

`\implies a^3+b^3`