Question

Simplify (x-y)^3 / x^2-y^2

Answer 1

Recall the identity $x^2-y^2=(x-y)(x+y)$

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

Cancel the common factor and get
$\frac{(x-y)^2}{x+y},~x\ne y$

Answer 2

The expression=(x-y)³/(x²-y²)
Since by factorizing x²-y² we get (x+y)(x-y) , the equation stands:
(x-y)³/((x+y)(x-y))
=(x-y)²/(x+y)
=(x²-2xy+y²)(x+y).
Ans)(x²-2xy+y²)(x+y).