Basic Math Examples

$\frac{- 4 a^{2} b + 8 a^{3} b^{2} - 12 a^{3} b}{- 4 a^{2} b}$

Step 1

Factor $4 a^{2} b$ out of $- 4 a^{2} b + 8 a^{3} b^{2} - 12 a^{3} b$ .

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Step 1.1

Factor $4 a^{2} b$ out of $- 4 a^{2} b$ .

$\frac{4 a^{2} b (- 1) + 8 a^{3} b^{2} - 12 a^{3} b}{- 4 a^{2} b}$

Step 1.2

Factor $4 a^{2} b$ out of $8 a^{3} b^{2}$ .

$\frac{4 a^{2} b (- 1) + 4 a^{2} b (2 a b) - 12 a^{3} b}{- 4 a^{2} b}$

Step 1.3

Factor $4 a^{2} b$ out of $- 12 a^{3} b$ .

$\frac{4 a^{2} b (- 1) + 4 a^{2} b (2 a b) + 4 a^{2} b (- 3 a)}{- 4 a^{2} b}$

Step 1.4

Factor $4 a^{2} b$ out of $4 a^{2} b (- 1) + 4 a^{2} b (2 a b)$ .

$\frac{4 a^{2} b (- 1 + 2 a b) + 4 a^{2} b (- 3 a)}{- 4 a^{2} b}$

Step 1.5

Factor $4 a^{2} b$ out of $4 a^{2} b (- 1 + 2 a b) + 4 a^{2} b (- 3 a)$ .

$\frac{4 a^{2} b (- 1 + 2 a b - 3 a)}{- 4 a^{2} b}$

Step 2

Cancel the common factor of $4$ and $- 4$ .

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Step 2.1

Factor $4$ out of $4 a^{2} b (- 1 + 2 a b - 3 a)$ .

$\frac{4 (a^{2} b (- 1 + 2 a b - 3 a))}{- 4 a^{2} b}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $4$ out of $- 4 a^{2} b$ .

$\frac{4 (a^{2} b (- 1 + 2 a b - 3 a))}{4 (- a^{2} b)}$

Step 2.2.2

Cancel the common factor.

$\frac{4 (a^{2} b (- 1 + 2 a b - 3 a))}{4 (- a^{2} b)}$

Step 2.2.3

Rewrite the expression.

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

Step 3

Cancel the common factor of $a^{2}$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

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

Step 4

Cancel the common factor of $b$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

$\frac{- 1 + 2 a b - 3 a}{- 1}$

Step 4.3

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

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

Step 5

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

$- (- 1 + 2 a b - 3 a)$

Step 6

Apply the distributive property.

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

Step 7

Simplify.

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Step 7.1

Multiply $- 1$ by $- 1$ .

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

Step 7.2

Multiply $2$ by $- 1$ .

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

Step 7.3

Multiply $- 3$ by $- 1$ .

$1 - 2 (a b) + 3 a$

$1 - 2 a b + 3 a$