Algebra Examples

$(18 m^{4} + 3 m^{3} + 45 m^{2}) \div 9 m$

Step 1

Rewrite the division as a fraction.

$\frac{18 m^{4} + 3 m^{3} + 45 m^{2}}{9 m}$

Step 2

Factor $3 m^{2}$ out of $18 m^{4} + 3 m^{3} + 45 m^{2}$ .

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Step 2.1

Factor $3 m^{2}$ out of $18 m^{4}$ .

$\frac{3 m^{2} (6 m^{2}) + 3 m^{3} + 45 m^{2}}{9 m}$

Step 2.2

Factor $3 m^{2}$ out of $3 m^{3}$ .

$\frac{3 m^{2} (6 m^{2}) + 3 m^{2} (m) + 45 m^{2}}{9 m}$

Step 2.3

Factor $3 m^{2}$ out of $45 m^{2}$ .

$\frac{3 m^{2} (6 m^{2}) + 3 m^{2} (m) + 3 m^{2} (15)}{9 m}$

Step 2.4

Factor $3 m^{2}$ out of $3 m^{2} (6 m^{2}) + 3 m^{2} (m)$ .

$\frac{3 m^{2} (6 m^{2} + m) + 3 m^{2} (15)}{9 m}$

Step 2.5

Factor $3 m^{2}$ out of $3 m^{2} (6 m^{2} + m) + 3 m^{2} (15)$ .

$\frac{3 m^{2} (6 m^{2} + m + 15)}{9 m}$

Step 3

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

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Step 3.1

Factor $3$ out of $3 m^{2} (6 m^{2} + m + 15)$ .

$\frac{3 (m^{2} (6 m^{2} + m + 15))}{9 m}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $3$ out of $9 m$ .

$\frac{3 (m^{2} (6 m^{2} + m + 15))}{3 (3 m)}$

Step 3.2.2

Cancel the common factor.

$\frac{3 (m^{2} (6 m^{2} + m + 15))}{3 (3 m)}$

Step 3.2.3

Rewrite the expression.

$\frac{m^{2} (6 m^{2} + m + 15)}{3 m}$

Step 4

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

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Step 4.1

Factor $m$ out of $m^{2} (6 m^{2} + m + 15)$ .

$\frac{m (m (6 m^{2} + m + 15))}{3 m}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $m$ out of $3 m$ .

$\frac{m (m (6 m^{2} + m + 15))}{m \cdot 3}$

Step 4.2.2

Cancel the common factor.

$\frac{m (m (6 m^{2} + m + 15))}{m \cdot 3}$

Step 4.2.3

Rewrite the expression.

$\frac{m (6 m^{2} + m + 15)}{3}$

Step 5

Apply the distributive property.

$\frac{m (6 m^{2}) + m \cdot m + m \cdot 15}{3}$

Step 6

Simplify.

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Step 6.1

Rewrite using the commutative property of multiplication.

$\frac{6 m \cdot m^{2} + m \cdot m + m \cdot 15}{3}$

Step 6.2

Multiply $m$ by $m$ .

$\frac{6 m \cdot m^{2} + m^{2} + m \cdot 15}{3}$

Step 6.3

Move $15$ to the left of $m$ .

$\frac{6 m \cdot m^{2} + m^{2} + 15 \cdot m}{3}$

Step 7

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

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Step 7.1

Move $m^{2}$ .

$\frac{6 (m^{2} m) + m^{2} + 15 \cdot m}{3}$

Step 7.2

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

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Step 7.2.1

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

$\frac{6 (m^{2} m^{1}) + m^{2} + 15 \cdot m}{3}$

Step 7.2.2

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

$\frac{6 m^{2 + 1} + m^{2} + 15 \cdot m}{3}$

Step 7.3

Add $2$ and $1$ .

$\frac{6 m^{3} + m^{2} + 15 \cdot m}{3}$

$\frac{6 m^{3} + m^{2} + 15 m}{3}$

Step 8

Split the fraction $\frac{6 m^{3} + m^{2} + 15 m}{3}$ into two fractions.

$\frac{6 m^{3} + m^{2}}{3} + \frac{15 m}{3}$

Step 9

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

$\frac{6 m^{3}}{3} + \frac{m^{2}}{3} + \frac{15 m}{3}$

Step 10

Cancel the common factor of $6$ and $3$ .

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Step 10.1

Factor $3$ out of $6 m^{3}$ .

$\frac{3 (2 m^{3})}{3} + \frac{m^{2}}{3} + \frac{15 m}{3}$

Step 10.2

Cancel the common factors.

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Step 10.2.1

Factor $3$ out of $3$ .

$\frac{3 (2 m^{3})}{3 (1)} + \frac{m^{2}}{3} + \frac{15 m}{3}$

Step 10.2.2

Cancel the common factor.

$\frac{3 (2 m^{3})}{3 \cdot 1} + \frac{m^{2}}{3} + \frac{15 m}{3}$

Step 10.2.3

Rewrite the expression.

$\frac{2 m^{3}}{1} + \frac{m^{2}}{3} + \frac{15 m}{3}$

Step 10.2.4

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

$2 m^{3} + \frac{m^{2}}{3} + \frac{15 m}{3}$

Step 11

Cancel the common factor of $15$ and $3$ .

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Step 11.1

Factor $3$ out of $15 m$ .

$2 m^{3} + \frac{m^{2}}{3} + \frac{3 (5 m)}{3}$

Step 11.2

Cancel the common factors.

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Step 11.2.1

Factor $3$ out of $3$ .

$2 m^{3} + \frac{m^{2}}{3} + \frac{3 (5 m)}{3 (1)}$

Step 11.2.2

Cancel the common factor.

$2 m^{3} + \frac{m^{2}}{3} + \frac{3 (5 m)}{3 \cdot 1}$

Step 11.2.3

Rewrite the expression.

$2 m^{3} + \frac{m^{2}}{3} + \frac{5 m}{1}$

Step 11.2.4

Divide $5 m$ by $1$ .

$2 m^{3} + \frac{m^{2}}{3} + 5 m$