Question

Sa se descompuna in factori expresia: (a la putere2+2ab-b la puterea2) totul la puterea 2 +(a puterea 2-2ab-b puterea 2) totul la puterea 2.

Answer 1

(a²+2ab-b²)² +(a²-2ab-b²)²=
=(a²+ab+ab-b²)² +(a²-ab-ab-b²)²=
=[a(a+b)+b(a-b)]² +[a(a-b)-b(a+b)]²=
=a²(a+b)²+b²(a-b)²+2ab(a+b)(a-b) +a²(a-b)²+b²(a+b)²-2ab(a+b)(a-b)=
=a²(a+b)²+b²(a-b)² +a²(a-b)²+b²(a+b)²=
=(a+b)²(a²+b²)+(a-b)²(a²+b²)=
=(a²+b²)[(a+b)²+(a-b)²]=
=(a²+b²)(a²+b²+2ab+a²+b²-2ab)=
=(a²+b²)(2a²+2b²)=
=(a²+b²)(2a²+2b²)=
=2(a²+b²)²