Algebra Examples

$4 (x - y) - 2 {(x - y)}^{2}$

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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

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

Step 2

Apply the distributive property.

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

Step 3

Multiply $- - y$ .

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Step 3.1

Multiply $- 1$ by $- 1$ .

$2 (x - y) (2 - x + 1 y)$

Step 3.2

Multiply $y$ by $1$ .

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

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

Step 4

Factor.

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Step 4.1

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

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Step 4.1.1

Move $2$ .

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

Step 4.1.2

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

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

Step 4.1.3

Factor $- 1$ out of $y$ .

$2 (x - y) (- (x) - 1 (- y) + 2)$

Step 4.1.4

Rewrite $2$ as $- 1 (- 2)$ .

$2 (x - y) (- (x) - 1 (- y) - 1 (- 2))$

Step 4.1.5

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

$2 (x - y) (- (x - y) - 1 (- 2))$

Step 4.1.6

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

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

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

Step 4.2

Remove unnecessary parentheses.

$2 (x - y) \cdot - 1 (x - y - 2)$

$2 (x - y) \cdot - 1 (x - y - 2)$

Step 5

Combine exponents.

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Step 5.1

Factor out negative.

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

Step 5.2

Multiply $2$ by $- 1$ .

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

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

Step 6

Remove unnecessary parentheses.

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

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$