Question

-x² + 2xy - y² / x+ y = ? / y² - x²

Answer 1

\(\dfrac{-x^2+2xy-y^2}{x+y}=\dfrac{-\left(x^2-2xy+y^2\right)}{x+y}=\dfrac{-\left(x-y\right)^2}{\left(x+y\right)}=\dfrac{-\left(x-y\right)^3}{\left(x+y\right)\left(x-y\right)}=\dfrac{-\left(x-y\right)^3}{x^2-y^2}=\dfrac{\left(x-y\right)^3}{y^2-x^2}\Rightarrow?=\left(x-y\right)^3\)

Answer 2

\(\dfrac{-x^2+2xy-y^2}{x+y}=\dfrac{?}{y^2-x^2}\)

\(\dfrac{-\left(x-y\right)^2}{x+y}=\dfrac{-?}{x^2-y^2}\)

\(\dfrac{-\left(x-y\right)^2}{x+y}=\dfrac{-?}{\left(x-y\right)\left(x+y\right)}\)

\(-?\left(x+y\right)=-\left(x-y\right)^3\left(x+y\right)\)

\(?=\left(x-y\right)^3\)