Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 2

Apply the distributive property.

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

Step 3

Multiply $- 2$ by $- 1$ .

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

Step 4

Subtract $x$ from $3 x$ .

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

Step 5

Factor.

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Step 5.1

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

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Step 5.1.1

Factor $2$ out of $2 x$ .

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

Step 5.1.2

Factor $2$ out of $2 y$ .

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

Step 5.1.3

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

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

Step 5.2

Remove unnecessary parentheses.

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