Basic Math Examples

$(9 a b - 18 a^{2} b^{2} + 36 a^{2} b^{3}) \div 3 a b$

Step 1

Rewrite the division as a fraction.

$\frac{9 a b - 18 a^{2} b^{2} + 36 a^{2} b^{3}}{3 a b}$

Step 2

Factor $9 a b$ out of $9 a b - 18 a^{2} b^{2} + 36 a^{2} b^{3}$ .

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Step 2.1

Factor $9 a b$ out of $9 a b$ .

$\frac{9 a b (1) - 18 a^{2} b^{2} + 36 a^{2} b^{3}}{3 a b}$

Step 2.2

Factor $9 a b$ out of $- 18 a^{2} b^{2}$ .

$\frac{9 a b (1) + 9 a b (- 2 a b) + 36 a^{2} b^{3}}{3 a b}$

Step 2.3

Factor $9 a b$ out of $36 a^{2} b^{3}$ .

$\frac{9 a b (1) + 9 a b (- 2 a b) + 9 a b (4 a b^{2})}{3 a b}$

Step 2.4

Factor $9 a b$ out of $9 a b (1) + 9 a b (- 2 a b)$ .

$\frac{9 a b (1 - 2 a b) + 9 a b (4 a b^{2})}{3 a b}$

Step 2.5

Factor $9 a b$ out of $9 a b (1 - 2 a b) + 9 a b (4 a b^{2})$ .

$\frac{9 a b (1 - 2 a b + 4 a b^{2})}{3 a b}$

Step 3

Cancel the common factor of $9$ and $3$ .

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Step 3.1

Factor $3$ out of $9 a b (1 - 2 a b + 4 a b^{2})$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $3$ out of $3 a b$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

Cancel the common factor of $a$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

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

Step 5

Cancel the common factor of $b$ .

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Step 5.1

Cancel the common factor.

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

Step 5.2

Divide $3 (1 - 2 a b + 4 a b^{2})$ by $1$ .

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

Step 6

Apply the distributive property.

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

Step 7

Simplify.

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Step 7.1

Multiply $3$ by $1$ .

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

Step 7.2

Multiply $- 2$ by $3$ .

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

Step 7.3

Multiply $4$ by $3$ .

$3 - 6 (a b) + 12 (a b^{2})$

Step 8

Remove parentheses.

$3 - 6 a b + 12 a b^{2}$

Step 9

Simplify the expression.

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Step 9.1

Move $3$ .

$- 6 a b + 12 a b^{2} + 3$

Step 9.2

Reorder $- 6 a b$ and $12 a b^{2}$ .

$12 a b^{2} - 6 a b + 3$