Pre-Algebra Examples

$(8 a^{4} b^{3} - 12 a^{7} b^{2} + 4 a^{2} b) \div 2 a^{4} b$

Step 1

Rewrite the division as a fraction.

$\frac{8 a^{4} b^{3} - 12 a^{7} b^{2} + 4 a^{2} b}{2 a^{4} b}$

Step 2

Factor $4 a^{2} b$ out of $8 a^{4} b^{3} - 12 a^{7} b^{2} + 4 a^{2} b$ .

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Step 2.1

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

$\frac{4 a^{2} b (2 a^{2} b^{2}) - 12 a^{7} b^{2} + 4 a^{2} b}{2 a^{4} b}$

Step 2.2

Factor $4 a^{2} b$ out of $- 12 a^{7} b^{2}$ .

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

Step 2.3

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

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

Step 2.4

Factor $4 a^{2} b$ out of $4 a^{2} b (2 a^{2} b^{2}) + 4 a^{2} b (- 3 a^{5} b)$ .

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

Step 2.5

Factor $4 a^{2} b$ out of $4 a^{2} b (2 a^{2} b^{2} - 3 a^{5} b) + 4 a^{2} b (1)$ .

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

Step 3

Cancel the common factor of $4$ and $2$ .

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Step 3.1

Factor $2$ out of $4 a^{2} b (2 a^{2} b^{2} - 3 a^{5} b + 1)$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

Cancel the common factor of $a^{2}$ and $a^{4}$ .

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Step 4.1

Factor $a^{2}$ out of $2 a^{2} b (2 a^{2} b^{2} - 3 a^{5} b + 1)$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 5

Cancel the common factor of $b$ .

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Step 5.1

Cancel the common factor.

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

Step 5.2

Rewrite the expression.

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

Step 6

Apply the distributive property.

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

Step 7

Simplify.

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Step 7.1

Multiply $2$ by $2$ .

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

Step 7.2

Multiply $- 3$ by $2$ .

$\frac{4 (a^{2} b^{2}) - 6 (a^{5} b) + 2 \cdot 1}{a^{2}}$

Step 7.3

Multiply $2$ by $1$ .

$\frac{4 (a^{2} b^{2}) - 6 (a^{5} b) + 2}{a^{2}}$

Step 8

Remove parentheses.

$\frac{4 a^{2} b^{2} - 6 a^{5} b + 2}{a^{2}}$

Step 9

Split the fraction $\frac{4 a^{2} b^{2} - 6 a^{5} b + 2}{a^{2}}$ into two fractions.

$\frac{4 a^{2} b^{2} - 6 a^{5} b}{a^{2}} + \frac{2}{a^{2}}$

Step 10

Split the fraction $\frac{4 a^{2} b^{2} - 6 a^{5} b}{a^{2}}$ into two fractions.

$\frac{4 a^{2} b^{2}}{a^{2}} + \frac{- 6 a^{5} b}{a^{2}} + \frac{2}{a^{2}}$

Step 11

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

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Step 11.1

Cancel the common factor.

$\frac{4 a^{2} b^{2}}{a^{2}} + \frac{- 6 a^{5} b}{a^{2}} + \frac{2}{a^{2}}$

Step 11.2

Divide $4 b^{2}$ by $1$ .

$4 b^{2} + \frac{- 6 a^{5} b}{a^{2}} + \frac{2}{a^{2}}$

Step 12

Cancel the common factor of $a^{5}$ and $a^{2}$ .

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Step 12.1

Factor $a^{2}$ out of $- 6 a^{5} b$ .

$4 b^{2} + \frac{a^{2} (- 6 a^{3} b)}{a^{2}} + \frac{2}{a^{2}}$

Step 12.2

Cancel the common factors.

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Step 12.2.1

Multiply by $1$ .

$4 b^{2} + \frac{a^{2} (- 6 a^{3} b)}{a^{2} \cdot 1} + \frac{2}{a^{2}}$

Step 12.2.2

Cancel the common factor.

$4 b^{2} + \frac{a^{2} (- 6 a^{3} b)}{a^{2} \cdot 1} + \frac{2}{a^{2}}$

Step 12.2.3

Rewrite the expression.

$4 b^{2} + \frac{- 6 a^{3} b}{1} + \frac{2}{a^{2}}$

Step 12.2.4

Divide $- 6 a^{3} b$ by $1$ .

$4 b^{2} - 6 a^{3} b + \frac{2}{a^{2}}$