Simplify (5x^2-10xy)/(2(2y-x)^3)

$\frac{5 x^{2} - 10 x y}{2 {(2 y - x)}^{3}}$

Step 1

Factor $5 x$ out of $5 x^{2} - 10 x y$ .

Factor $5 x$ out of $5 x^{2}$ .

$\frac{5 x (x) - 10 x y}{2 {(2 y - x)}^{3}}$

Factor $5 x$ out of $- 10 x y$ .

$\frac{5 x (x) + 5 x (- 2 y)}{2 {(2 y - x)}^{3}}$

Factor $5 x$ out of $5 x (x) + 5 x (- 2 y)$ .

$\frac{5 x (x - 2 y)}{2 {(2 y - x)}^{3}}$

Step 2

Cancel the common factor of $x - 2 y$ and ${(2 y - x)}^{3}$ .

Factor $- 1$ out of $x$ .

$\frac{5 x (- 1 (- x) - 2 y)}{2 {(2 y - x)}^{3}}$

Factor $- 1$ out of $- 2 y$ .

$\frac{5 x (- 1 (- x) - (2 y))}{2 {(2 y - x)}^{3}}$

Factor $- 1$ out of $- 1 (- x) - (2 y)$ .

$\frac{5 x (- 1 (- x + 2 y))}{2 {(2 y - x)}^{3}}$

Reorder terms.

$\frac{5 x (- 1 (- x + 2 y))}{2 {(- x + 2 y)}^{3}}$

Factor $- x + 2 y$ out of $5 x (- 1 (- x + 2 y))$ .

$\frac{(- x + 2 y) (5 x \cdot (- 1))}{2 {(- x + 2 y)}^{3}}$

Cancel the common factors.

Factor $- x + 2 y$ out of $2 {(- x + 2 y)}^{3}$ .

$\frac{(- x + 2 y) (5 x \cdot (- 1))}{(- x + 2 y) (2 {(- x + 2 y)}^{2})}$

Cancel the common factor.

$\frac{(- x + 2 y) (5 x \cdot (- 1))}{(- x + 2 y) (2 {(- x + 2 y)}^{2})}$

Rewrite the expression.

$\frac{5 x \cdot (- 1)}{2 {(- x + 2 y)}^{2}}$

Step 3

Simplify the expression.

Multiply $- 1$ by $5$ .

$\frac{- 5 x}{2 {(- x + 2 y)}^{2}}$

Move the negative in front of the fraction.

$- \frac{5 x}{2 {(- x + 2 y)}^{2}}$