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

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

Step 1

Cancel the common factor of ${(x - y)}^{2}$ and $x - y$ .

Factor $x - y$ out of $2 x y {(x - y)}^{2}$ .

$\frac{(x - y) (2 x y (x - y))}{x - y}$

Cancel the common factors.

Multiply by $1$ .

$\frac{(x - y) (2 x y (x - y))}{(x - y) \cdot 1}$

Cancel the common factor.

$\frac{(x - y) (2 x y (x - y))}{(x - y) \cdot 1}$

Rewrite the expression.

$\frac{2 x y (x - y)}{1}$

Divide $2 x y (x - y)$ by $1$ .

$2 x y (x - y)$

$2 x y (x - y)$

$2 x y (x - y)$

Step 2

Apply the distributive property.

$2 x y x + 2 x y (- y)$

Step 3

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$2 (x \cdot x) y + 2 x y (- y)$

Multiply $x$ by $x$ .

$2 x^{2} y + 2 x y (- y)$

$2 x^{2} y + 2 x y (- y)$

Step 4

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$2 x^{2} y + 2 x (y \cdot y) \cdot - 1$

Multiply $y$ by $y$ .

$2 x^{2} y + 2 x y^{2} \cdot - 1$

$2 x^{2} y + 2 x y^{2} \cdot - 1$

Step 5

Multiply $- 1$ by $2$ .

$2 x^{2} y - 2 x y^{2}$

Related Questions