Algebra Examples

$\frac{6 a^{2} b - 12 a b^{2}}{- 2 a b}$

Step 1

Factor $6 a b$ out of $6 a^{2} b - 12 a b^{2}$ .

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Step 1.1

Factor $6 a b$ out of $6 a^{2} b$ .

$\frac{6 a b (a) - 12 a b^{2}}{- 2 a b}$

Step 1.2

Factor $6 a b$ out of $- 12 a b^{2}$ .

$\frac{6 a b (a) + 6 a b (- 2 b)}{- 2 a b}$

Step 1.3

Factor $6 a b$ out of $6 a b (a) + 6 a b (- 2 b)$ .

$\frac{6 a b (a - 2 b)}{- 2 a b}$

Step 2

Cancel the common factor of $6$ and $- 2$ .

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Step 2.1

Factor $2$ out of $6 a b (a - 2 b)$ .

$\frac{2 (3 a b (a - 2 b))}{- 2 a b}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $- 2 a b$ .

$\frac{2 (3 a b (a - 2 b))}{2 (- a b)}$

Step 2.2.2

Cancel the common factor.

$\frac{2 (3 a b (a - 2 b))}{2 (- a b)}$

Step 2.2.3

Rewrite the expression.

$\frac{3 a b (a - 2 b)}{- a b}$

Step 3

Cancel the common factor of $a$ .

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Step 3.1

Cancel the common factor.

$\frac{3 a b (a - 2 b)}{- a b}$

Step 3.2

Rewrite the expression.

$\frac{3 b (a - 2 b)}{- 1 b}$

Step 4

Cancel the common factor of $b$ .

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Step 4.1

Cancel the common factor.

$\frac{3 b (a - 2 b)}{- 1 b}$

Step 4.2

Rewrite the expression.

$\frac{3 (a - 2 b)}{- 1}$

Step 4.3

Move the negative one from the denominator of $\frac{3 (a - 2 b)}{- 1}$ .

$- 1 \cdot (3 (a - 2 b))$

Step 5

Rewrite $- 1 \cdot (3 (a - 2 b))$ as $- (3 (a - 2 b))$ .

$- (3 (a - 2 b))$

Step 6

Apply the distributive property.

$- (3 a + 3 (- 2 b))$

Step 7

Multiply $- 2$ by $3$ .

$- (3 a - 6 b)$

Step 8

Apply the distributive property.

$- (3 a) - (- 6 b)$

Step 9

Multiply $3$ by $- 1$ .

$- 3 a - (- 6 b)$

Step 10

Multiply $- 6$ by $- 1$ .

$- 3 a + 6 b$