Basic Math Examples

$\frac{12 m^{4} + 15 m^{3}}{3 m}$

Step 1

Factor $3 m^{3}$ out of $12 m^{4} + 15 m^{3}$ .

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Step 1.1

Factor $3 m^{3}$ out of $12 m^{4}$ .

$\frac{3 m^{3} (4 m) + 15 m^{3}}{3 m}$

Step 1.2

Factor $3 m^{3}$ out of $15 m^{3}$ .

$\frac{3 m^{3} (4 m) + 3 m^{3} (5)}{3 m}$

Step 1.3

Factor $3 m^{3}$ out of $3 m^{3} (4 m) + 3 m^{3} (5)$ .

$\frac{3 m^{3} (4 m + 5)}{3 m}$

Step 2

Cancel the common factor of $3$ .

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Step 2.1

Cancel the common factor.

$\frac{3 m^{3} (4 m + 5)}{3 m}$

Step 2.2

Rewrite the expression.

$\frac{m^{3} (4 m + 5)}{m}$

Step 3

Cancel the common factor of $m^{3}$ and $m$ .

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Step 3.1

Factor $m$ out of $m^{3} (4 m + 5)$ .

$\frac{m (m^{2} (4 m + 5))}{m}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$\frac{m (m^{2} (4 m + 5))}{m^{1}}$

Step 3.2.2

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

$\frac{m (m^{2} (4 m + 5))}{m \cdot 1}$

Step 3.2.3

Cancel the common factor.

$\frac{m (m^{2} (4 m + 5))}{m \cdot 1}$

Step 3.2.4

Rewrite the expression.

$\frac{m^{2} (4 m + 5)}{1}$

Step 3.2.5

Divide $m^{2} (4 m + 5)$ by $1$ .

$m^{2} (4 m + 5)$

Step 4

Apply the distributive property.

$m^{2} (4 m) + m^{2} \cdot 5$

Step 5

Rewrite using the commutative property of multiplication.

$4 m^{2} m + m^{2} \cdot 5$

Step 6

Move $5$ to the left of $m^{2}$ .

$4 m^{2} m + 5 \cdot m^{2}$

Step 7

Multiply $m^{2}$ by $m$ by adding the exponents.

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Step 7.1

Move $m$ .

$4 (m \cdot m^{2}) + 5 \cdot m^{2}$

Step 7.2

Multiply $m$ by $m^{2}$ .

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Step 7.2.1

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

$4 (m^{1} m^{2}) + 5 \cdot m^{2}$

Step 7.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 m^{1 + 2} + 5 \cdot m^{2}$

Step 7.3

Add $1$ and $2$ .

$4 m^{3} + 5 \cdot m^{2}$

$4 m^{3} + 5 m^{2}$