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

Answer:

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

Step-by-step 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:

$\implies a^3+b^3$