Question

Сократите дробь:
$frac{x^4-y^4}{x^3+xy^2-x^2y-y^3}$

Answer 1

$frac{x^4-y^4}{x^3+xy^2-x^2y-y^3}= frac{(x^2-y^2)(x^2+y^2)}{(x^3-x^2y)+(xy^2-y^3)}= frac{(x^2-y^2)(x^2+y^2)}{x^2(x-y)+y^2(x-y)}=$
$=frac{(x^2-y^2)(x^2+y^2)}{(x-y)(x^2+y^2)}= frac{x^2-y^2}{x-y} = frac{(x-y)(x+y)}{x-y} =x+y$