Question

a3+b3=
a3-b3=
(a+b)2+(a-b)=

Answer 1

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

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

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

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

= a^2+b^2 +a^2 +b^2

= 2a^2+ 2b^2

= 2(a^2+b^2)