Pre-Algebra Examples

$\frac{12 m + 24 m^{2} + 24 m^{3}}{4 m^{2}}$

Step 1

Factor $12 m$ out of $12 m + 24 m^{2} + 24 m^{3}$ .

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Step 1.1

Factor $12 m$ out of $12 m$ .

$\frac{12 m (1) + 24 m^{2} + 24 m^{3}}{4 m^{2}}$

Step 1.2

Factor $12 m$ out of $24 m^{2}$ .

$\frac{12 m (1) + 12 m (2 m) + 24 m^{3}}{4 m^{2}}$

Step 1.3

Factor $12 m$ out of $24 m^{3}$ .

$\frac{12 m (1) + 12 m (2 m) + 12 m (2 m^{2})}{4 m^{2}}$

Step 1.4

Factor $12 m$ out of $12 m (1) + 12 m (2 m)$ .

$\frac{12 m (1 + 2 m) + 12 m (2 m^{2})}{4 m^{2}}$

Step 1.5

Factor $12 m$ out of $12 m (1 + 2 m) + 12 m (2 m^{2})$ .

$\frac{12 m (1 + 2 m + 2 m^{2})}{4 m^{2}}$

Step 2

Cancel the common factor of $12$ and $4$ .

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Step 2.1

Factor $4$ out of $12 m (1 + 2 m + 2 m^{2})$ .

$\frac{4 (3 m (1 + 2 m + 2 m^{2}))}{4 m^{2}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $4$ out of $4 m^{2}$ .

$\frac{4 (3 m (1 + 2 m + 2 m^{2}))}{4 (m^{2})}$

Step 2.2.2

Cancel the common factor.

$\frac{4 (3 m (1 + 2 m + 2 m^{2}))}{4 m^{2}}$

Step 2.2.3

Rewrite the expression.

$\frac{3 m (1 + 2 m + 2 m^{2})}{m^{2}}$

Step 3

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

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Step 3.1

Factor $m$ out of $3 m (1 + 2 m + 2 m^{2})$ .

$\frac{m (3 (1 + 2 m + 2 m^{2}))}{m^{2}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $m$ out of $m^{2}$ .

$\frac{m (3 (1 + 2 m + 2 m^{2}))}{m \cdot m}$

Step 3.2.2

Cancel the common factor.

$\frac{m (3 (1 + 2 m + 2 m^{2}))}{m \cdot m}$

Step 3.2.3

Rewrite the expression.

$\frac{3 (1 + 2 m + 2 m^{2})}{m}$

Step 4

Apply the distributive property.

$\frac{3 \cdot 1 + 3 (2 m) + 3 (2 m^{2})}{m}$

Step 5

Simplify.

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Step 5.1

Multiply $3$ by $1$ .

$\frac{3 + 3 (2 m) + 3 (2 m^{2})}{m}$

Step 5.2

Multiply $2$ by $3$ .

$\frac{3 + 6 m + 3 (2 m^{2})}{m}$

Step 5.3

Multiply $2$ by $3$ .

$\frac{3 + 6 m + 6 m^{2}}{m}$

Step 6

Split the fraction $\frac{3 + 6 m + 6 m^{2}}{m}$ into two fractions.

$\frac{3 + 6 m}{m} + \frac{6 m^{2}}{m}$

Step 7

Split the fraction $\frac{3 + 6 m}{m}$ into two fractions.

$\frac{3}{m} + \frac{6 m}{m} + \frac{6 m^{2}}{m}$

Step 8

Cancel the common factor of $m$ .

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Step 8.1

Cancel the common factor.

$\frac{3}{m} + \frac{6 m}{m} + \frac{6 m^{2}}{m}$

Step 8.2

Divide $6$ by $1$ .

$\frac{3}{m} + 6 + \frac{6 m^{2}}{m}$

Step 9

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

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Step 9.1

Factor $m$ out of $6 m^{2}$ .

$\frac{3}{m} + 6 + \frac{m (6 m)}{m}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Raise $m$ to the power of $1$ .

$\frac{3}{m} + 6 + \frac{m (6 m)}{m^{1}}$

Step 9.2.2

Factor $m$ out of $m^{1}$ .

$\frac{3}{m} + 6 + \frac{m (6 m)}{m \cdot 1}$

Step 9.2.3

Cancel the common factor.

$\frac{3}{m} + 6 + \frac{m (6 m)}{m \cdot 1}$

Step 9.2.4

Rewrite the expression.

$\frac{3}{m} + 6 + \frac{6 m}{1}$

Step 9.2.5

Divide $6 m$ by $1$ .

$\frac{3}{m} + 6 + 6 m$