Pre-Algebra Examples

$\frac{- 30 a^{2} b^{2} - 25 a^{2} b - 40 a b^{2}}{- 10 a b}$

Step 1

Factor $5 a b$ out of $- 30 a^{2} b^{2} - 25 a^{2} b - 40 a b^{2}$ .

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Step 1.1

Factor $5 a b$ out of $- 30 a^{2} b^{2}$ .

$\frac{5 a b (- 6 a b) - 25 a^{2} b - 40 a b^{2}}{- 10 a b}$

Step 1.2

Factor $5 a b$ out of $- 25 a^{2} b$ .

$\frac{5 a b (- 6 a b) + 5 a b (- 5 a) - 40 a b^{2}}{- 10 a b}$

Step 1.3

Factor $5 a b$ out of $- 40 a b^{2}$ .

$\frac{5 a b (- 6 a b) + 5 a b (- 5 a) + 5 a b (- 8 b)}{- 10 a b}$

Step 1.4

Factor $5 a b$ out of $5 a b (- 6 a b) + 5 a b (- 5 a)$ .

$\frac{5 a b (- 6 a b - 5 a) + 5 a b (- 8 b)}{- 10 a b}$

Step 1.5

Factor $5 a b$ out of $5 a b (- 6 a b - 5 a) + 5 a b (- 8 b)$ .

$\frac{5 a b (- 6 a b - 5 a - 8 b)}{- 10 a b}$

Step 2

Cancel the common factor of $5$ and $- 10$ .

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Step 2.1

Factor $5$ out of $5 a b (- 6 a b - 5 a - 8 b)$ .

$\frac{5 (a b (- 6 a b - 5 a - 8 b))}{- 10 a b}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $5$ out of $- 10 a b$ .

$\frac{5 (a b (- 6 a b - 5 a - 8 b))}{5 (- 2 a b)}$

Step 2.2.2

Cancel the common factor.

$\frac{5 (a b (- 6 a b - 5 a - 8 b))}{5 (- 2 a b)}$

Step 2.2.3

Rewrite the expression.

$\frac{a b (- 6 a b - 5 a - 8 b)}{- 2 a b}$

Step 3

Cancel the common factor of $a$ .

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Step 3.1

Cancel the common factor.

$\frac{a b (- 6 a b - 5 a - 8 b)}{- 2 a b}$

Step 3.2

Rewrite the expression.

$\frac{b (- 6 a b - 5 a - 8 b)}{- 2 b}$

Step 4

Cancel the common factor of $b$ .

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Step 4.1

Cancel the common factor.

$\frac{b (- 6 a b - 5 a - 8 b)}{- 2 b}$

Step 4.2

Rewrite the expression.

$\frac{- 6 a b - 5 a - 8 b}{- 2}$

Step 5

Move the negative in front of the fraction.

$- \frac{- 6 a b - 5 a - 8 b}{2}$

Step 6

Factor $- 1$ out of $- 6 a b$ .

$- \frac{- (6 a b) - 5 a - 8 b}{2}$

Step 7

Factor $- 1$ out of $- 5 a$ .

$- \frac{- (6 a b) - (5 a) - 8 b}{2}$

Step 8

Factor $- 1$ out of $- (6 a b) - (5 a)$ .

$- \frac{- (6 a b + 5 a) - 8 b}{2}$

Step 9

Factor $- 1$ out of $- 8 b$ .

$- \frac{- (6 a b + 5 a) - (8 b)}{2}$

Step 10

Factor $- 1$ out of $- (6 a b + 5 a) - (8 b)$ .

$- \frac{- (6 a b + 5 a + 8 b)}{2}$

Step 11

Rewrite $- (6 a b + 5 a + 8 b)$ as $- 1 (6 a b + 5 a + 8 b)$ .

$- \frac{- 1 (6 a b + 5 a + 8 b)}{2}$

Step 12

Move the negative in front of the fraction.

$- - \frac{6 a b + 5 a + 8 b}{2}$

Step 13

Multiply $- 1$ by $- 1$ .

$1 \frac{6 a b + 5 a + 8 b}{2}$

Step 14

Multiply $\frac{6 a b + 5 a + 8 b}{2}$ by $1$ .

$\frac{6 a b + 5 a + 8 b}{2}$

Step 15

Split the fraction $\frac{6 a b + 5 a + 8 b}{2}$ into two fractions.

$\frac{6 a b + 5 a}{2} + \frac{8 b}{2}$

Step 16

Split the fraction $\frac{6 a b + 5 a}{2}$ into two fractions.

$\frac{6 a b}{2} + \frac{5 a}{2} + \frac{8 b}{2}$

Step 17

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

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Step 17.1

Factor $2$ out of $6 a b$ .

$\frac{2 (3 a b)}{2} + \frac{5 a}{2} + \frac{8 b}{2}$

Step 17.2

Cancel the common factors.

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Step 17.2.1

Factor $2$ out of $2$ .

$\frac{2 (3 a b)}{2 (1)} + \frac{5 a}{2} + \frac{8 b}{2}$

Step 17.2.2

Cancel the common factor.

$\frac{2 (3 a b)}{2 \cdot 1} + \frac{5 a}{2} + \frac{8 b}{2}$

Step 17.2.3

Rewrite the expression.

$\frac{3 a b}{1} + \frac{5 a}{2} + \frac{8 b}{2}$

Step 17.2.4

Divide $3 a b$ by $1$ .

$3 a b + \frac{5 a}{2} + \frac{8 b}{2}$

Step 18

Cancel the common factor of $8$ and $2$ .

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Step 18.1

Factor $2$ out of $8 b$ .

$3 a b + \frac{5 a}{2} + \frac{2 (4 b)}{2}$

Step 18.2

Cancel the common factors.

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Step 18.2.1

Factor $2$ out of $2$ .

$3 a b + \frac{5 a}{2} + \frac{2 (4 b)}{2 (1)}$

Step 18.2.2

Cancel the common factor.

$3 a b + \frac{5 a}{2} + \frac{2 (4 b)}{2 \cdot 1}$

Step 18.2.3

Rewrite the expression.

$3 a b + \frac{5 a}{2} + \frac{4 b}{1}$

Step 18.2.4

Divide $4 b$ by $1$ .

$3 a b + \frac{5 a}{2} + 4 b$