Algebra Examples

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

Step 1

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

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Step 1.1

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

$(x - 2 y) (x - 2 y) - 3 x (x - 2 y)$

Step 1.2

Factor $x - 2 y$ out of $- 3 x (x - 2 y)$ .

$(x - 2 y) (x - 2 y) + (x - 2 y) (- 3 x)$

Step 1.3

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

$(x - 2 y) (x - 2 y - 3 x)$

$(x - 2 y) (x - 2 y - 3 x)$

Step 2

Subtract $3 x$ from $x$ .

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

Step 3

Factor.

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Step 3.1

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

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Step 3.1.1

Factor $2$ out of $- 2 x$ .

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

Step 3.1.2

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

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

Step 3.1.3

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

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

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

Step 3.2

Remove unnecessary parentheses.

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

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

Step 4

Factor.

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Step 4.1

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

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Step 4.1.1

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

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

Step 4.1.2

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

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

Step 4.1.3

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

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

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

Step 4.2

Remove unnecessary parentheses.

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

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

Step 5

Combine exponents.

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Step 5.1

Factor out negative.

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

Step 5.2

Multiply $2$ by $- 1$ .

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

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

Step 6

Remove unnecessary parentheses.

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

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