Question

calcule: (x+y)² . (x-y)²

Answer 1

= (x+y)² . (x-y)²
= ( x^2 + 2xy +y^2). (x^2 - 2xy + y^2)
= x^2.x^2 - 2xy.x^2 + x^2.y^2 + 2xy.x^2 - 2xy.2xy +2xy.y^2 + x^2.y^2 - 2xy.y^2 + y^2. y^2
= x^4 - 2x^3y + x^2y^2 + 2x^3y - 4x^2y^2 + 2xy^3 + x^2y^2 - 2xy^3 + y^4
= x^4 + y^4 - 2x^3y + 2x^3y + x^2y^2 + x^2y^2 + 4x^2y^2 + 2xy^3 - 2xy^3
= x^4 + y^4 + 6x^2y^2