Question

a^3+b^3=(a+b) (a^2-ab + b^2)​

Answer 1

Answer:

How is (a^3 +b^3)=(a+b) (a^2 -ab+ b^2)?

Taking RHS: (a+b)(a^2-ab+b^2)

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

= a^3 -a^2b+ab^2 + a^2b-ab^2+b^3

= a^3 + b^3

= LHS

Edit: Swathi Annamaneni, Sure, Justwork my solution backwards

LHS = a^3 + b^3

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

= RHS (on rearranging and taking out the factors)

Answer 2

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

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

=a^3-a^2b+ab^2+ba^2-ab^3 + b^3

= a^3+b^3= RHS