Pre-Algebra Examples

$(18 a^{7} b^{3} - 30 a^{9} b^{2} + 12 a^{2} b) \div 6 a^{7} b$

Step 1

Rewrite the division as a fraction.

$\frac{18 a^{7} b^{3} - 30 a^{9} b^{2} + 12 a^{2} b}{6 a^{7} b}$

Step 2

Factor $6 a^{2} b$ out of $18 a^{7} b^{3} - 30 a^{9} b^{2} + 12 a^{2} b$ .

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Step 2.1

Factor $6 a^{2} b$ out of $18 a^{7} b^{3}$ .

$\frac{6 a^{2} b (3 a^{5} b^{2}) - 30 a^{9} b^{2} + 12 a^{2} b}{6 a^{7} b}$

Step 2.2

Factor $6 a^{2} b$ out of $- 30 a^{9} b^{2}$ .

$\frac{6 a^{2} b (3 a^{5} b^{2}) + 6 a^{2} b (- 5 a^{7} b) + 12 a^{2} b}{6 a^{7} b}$

Step 2.3

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

$\frac{6 a^{2} b (3 a^{5} b^{2}) + 6 a^{2} b (- 5 a^{7} b) + 6 a^{2} b (2)}{6 a^{7} b}$

Step 2.4

Factor $6 a^{2} b$ out of $6 a^{2} b (3 a^{5} b^{2}) + 6 a^{2} b (- 5 a^{7} b)$ .

$\frac{6 a^{2} b (3 a^{5} b^{2} - 5 a^{7} b) + 6 a^{2} b (2)}{6 a^{7} b}$

Step 2.5

Factor $6 a^{2} b$ out of $6 a^{2} b (3 a^{5} b^{2} - 5 a^{7} b) + 6 a^{2} b (2)$ .

$\frac{6 a^{2} b (3 a^{5} b^{2} - 5 a^{7} b + 2)}{6 a^{7} b}$

Step 3

Cancel the common factor of $6$ .

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Step 3.1

Cancel the common factor.

$\frac{6 a^{2} b (3 a^{5} b^{2} - 5 a^{7} b + 2)}{6 a^{7} b}$

Step 3.2

Rewrite the expression.

$\frac{a^{2} b (3 a^{5} b^{2} - 5 a^{7} b + 2)}{a^{7} b}$

Step 4

Cancel the common factor of $a^{2}$ and $a^{7}$ .

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Step 4.1

Factor $a^{2}$ out of $a^{2} b (3 a^{5} b^{2} - 5 a^{7} b + 2)$ .

$\frac{a^{2} (b (3 a^{5} b^{2} - 5 a^{7} b + 2))}{a^{7} b}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $a^{2}$ out of $a^{7} b$ .

$\frac{a^{2} (b (3 a^{5} b^{2} - 5 a^{7} b + 2))}{a^{2} (a^{5} b)}$

Step 4.2.2

Cancel the common factor.

$\frac{a^{2} (b (3 a^{5} b^{2} - 5 a^{7} b + 2))}{a^{2} (a^{5} b)}$

Step 4.2.3

Rewrite the expression.

$\frac{b (3 a^{5} b^{2} - 5 a^{7} b + 2)}{a^{5} b}$

Step 5

Cancel the common factor of $b$ .

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Step 5.1

Cancel the common factor.

$\frac{b (3 a^{5} b^{2} - 5 a^{7} b + 2)}{a^{5} b}$

Step 5.2

Rewrite the expression.

$\frac{3 a^{5} b^{2} - 5 a^{7} b + 2}{a^{5}}$

Step 6

Split the fraction $\frac{3 a^{5} b^{2} - 5 a^{7} b + 2}{a^{5}}$ into two fractions.

$\frac{3 a^{5} b^{2} - 5 a^{7} b}{a^{5}} + \frac{2}{a^{5}}$

Step 7

Split the fraction $\frac{3 a^{5} b^{2} - 5 a^{7} b}{a^{5}}$ into two fractions.

$\frac{3 a^{5} b^{2}}{a^{5}} + \frac{- 5 a^{7} b}{a^{5}} + \frac{2}{a^{5}}$

Step 8

Cancel the common factor of $a^{5}$ .

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Step 8.1

Cancel the common factor.

$\frac{3 a^{5} b^{2}}{a^{5}} + \frac{- 5 a^{7} b}{a^{5}} + \frac{2}{a^{5}}$

Step 8.2

Divide $3 b^{2}$ by $1$ .

$3 b^{2} + \frac{- 5 a^{7} b}{a^{5}} + \frac{2}{a^{5}}$

Step 9

Cancel the common factor of $a^{7}$ and $a^{5}$ .

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Step 9.1

Factor $a^{5}$ out of $- 5 a^{7} b$ .

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

Step 9.2

Cancel the common factors.

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Step 9.2.1

Multiply by $1$ .

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

Step 9.2.2

Cancel the common factor.

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

Step 9.2.3

Rewrite the expression.

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

Step 9.2.4

Divide $- 5 a^{2} b$ by $1$ .

$3 b^{2} - 5 a^{2} b + \frac{2}{a^{5}}$