Question

Resolva: (x+y)³ - 2y (y+x)² / x² - y²

Answer 1

Oi!

$\\ \displaystyle \mathsf{\frac{(x + y)^3 - 2y(x + y)^2}{x^2 - y^2} =} \\\\\\ \mathsf{\frac{(x + y)^2 \cdot \left [ (x + y)^1 - 2y \right ]}{(x + y)(x - y)} =} \\\\\\ \mathsf{\frac{(x + y)^2 \cdot (x + y - 2y)}{(x + y)(x - y)} =} \\\\\\ \mathsf{\frac{(x + y)(x + y)(x - y)}{(x + y)(x - y)} =} \\\\\\ \boxed{\mathsf{x + y}}$

 Sempre que, $\mathsf{x^2 - y^2 \neq 0 \Rightarrow x \neq \pm y}$.