Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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 ${(2 y - x)}^{3}$ .

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Step 2.1

Factor $- 1$ out of $x$ .

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

Reorder terms.

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

Step 2.5

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

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

Step 2.6

Cancel the common factors.

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Step 2.6.1

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

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

Step 2.6.2

Cancel the common factor.

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

Step 2.6.3

Rewrite the expression.

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

Step 3

Simplify the expression.

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Step 3.1

Multiply $- 1$ by $5$ .

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

Step 3.2

Move the negative in front of the fraction.

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