Algebra Examples

$\frac{8 x^{3} y^{4} {(x - y)}^{2}}{12 x^{2} y^{5} (y - x)}$

Step 1

Cancel the common factor of $8$ and $12$ .

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Step 1.1

Factor $4$ out of $8 x^{3} y^{4} {(x - y)}^{2}$ .

$\frac{4 (2 x^{3} y^{4} {(x - y)}^{2})}{12 x^{2} y^{5} (y - x)}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $4$ out of $12 x^{2} y^{5} (y - x)$ .

$\frac{4 (2 x^{3} y^{4} {(x - y)}^{2})}{4 (3 x^{2} y^{5} (y - x))}$

Step 1.2.2

Cancel the common factor.

$\frac{4 (2 x^{3} y^{4} {(x - y)}^{2})}{4 (3 x^{2} y^{5} (y - x))}$

Step 1.2.3

Rewrite the expression.

$\frac{2 x^{3} y^{4} {(x - y)}^{2}}{3 x^{2} y^{5} (y - x)}$

Step 2

Cancel the common factor of $x^{3}$ and $x^{2}$ .

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Step 2.1

Factor $x^{2}$ out of $2 x^{3} y^{4} {(x - y)}^{2}$ .

$\frac{x^{2} (2 x y^{4} {(x - y)}^{2})}{3 x^{2} y^{5} (y - x)}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $x^{2}$ out of $3 x^{2} y^{5} (y - x)$ .

$\frac{x^{2} (2 x y^{4} {(x - y)}^{2})}{x^{2} (3 y^{5} (y - x))}$

Step 2.2.2

Cancel the common factor.

$\frac{x^{2} (2 x y^{4} {(x - y)}^{2})}{x^{2} (3 y^{5} (y - x))}$

Step 2.2.3

Rewrite the expression.

$\frac{2 x y^{4} {(x - y)}^{2}}{3 y^{5} (y - x)}$

Step 3

Cancel the common factor of $y^{4}$ and $y^{5}$ .

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Step 3.1

Factor $y^{4}$ out of $2 x y^{4} {(x - y)}^{2}$ .

$\frac{y^{4} (2 x {(x - y)}^{2})}{3 y^{5} (y - x)}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $y^{4}$ out of $3 y^{5} (y - x)$ .

$\frac{y^{4} (2 x {(x - y)}^{2})}{y^{4} (3 y (y - x))}$

Step 3.2.2

Cancel the common factor.

$\frac{y^{4} (2 x {(x - y)}^{2})}{y^{4} (3 y (y - x))}$

Step 3.2.3

Rewrite the expression.

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

Step 4

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

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Step 4.1

Factor $- 1$ out of $x$ .

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

Step 4.2

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

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

Step 4.3

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

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

Step 4.4

Apply the product rule to $- 1 (- x + y)$ .

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

Step 4.5

Raise $- 1$ to the power of $2$ .

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

Step 4.6

Multiply ${(- x + y)}^{2}$ by $1$ .

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

Step 4.7

Reorder terms.

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

Step 4.8

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

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

Step 4.9

Cancel the common factors.

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Step 4.9.1

Factor $- x + y$ out of $3 y (- x + y)$ .

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

Step 4.9.2

Cancel the common factor.

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

Step 4.9.3

Rewrite the expression.

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

Step 5

Factor $- 1$ out of $- x$ .

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

Step 6

Factor $- 1$ out of $y$ .

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

Step 7

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

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

Step 8

Simplify the expression.

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Step 8.1

Rewrite $- (x - y)$ as $- 1 (x - y)$ .

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

Step 8.2

Move the negative in front of the fraction.

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

Step 8.3

Reorder factors in $- \frac{(2 x) (x - y)}{3 y}$ .

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