Question

(a^2 + b^2)^2 + (a^8 + b^8)^2

Answer 1

a^4+2ab^2+b^4+a^16+2ab^8+b^16

Explanation:

(a^2+b^2)^2+(a^8+b^8)^2

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

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

=a^4+(ab)^2+(ba)^2+b^4

=a^4+2ab^2+b^4

(a^8+b^8)^2=(a^8+b^8)(a^8+b^8)

=a^8(a^8+b^8)+b^8(a^8+b^8)

=a^16+(ab)^8+(ba)^8+b^16

=a^16+2ab^8+b^16

(a^2+b^2)^2+(a^8+b^8)^2=(a^4+2ab^2+b^4)+(a^16+2ab^8+b^16)

the answer is a^4+2ab^2+b^4+a^16+2ab^8+b^16

i think it is simplified answer