Algebra Examples

$(24 k^{3} + 2 k^{2} + 24 k) \div 6$

Step 1

Rewrite the division as a fraction.

$\frac{24 k^{3} + 2 k^{2} + 24 k}{6}$

Step 2

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

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Step 2.1

Factor $2 k$ out of $24 k^{3}$ .

$\frac{2 k (12 k^{2}) + 2 k^{2} + 24 k}{6}$

Step 2.2

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

$\frac{2 k (12 k^{2}) + 2 k (k) + 24 k}{6}$

Step 2.3

Factor $2 k$ out of $24 k$ .

$\frac{2 k (12 k^{2}) + 2 k (k) + 2 k (12)}{6}$

Step 2.4

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

$\frac{2 k (12 k^{2} + k) + 2 k (12)}{6}$

Step 2.5

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

$\frac{2 k (12 k^{2} + k + 12)}{6}$

Step 3

Cancel the common factor of $2$ and $6$ .

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Step 3.1

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

$\frac{2 (k (12 k^{2} + k + 12))}{6}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $6$ .

$\frac{2 (k (12 k^{2} + k + 12))}{2 \cdot 3}$

Step 3.2.2

Cancel the common factor.

$\frac{2 (k (12 k^{2} + k + 12))}{2 \cdot 3}$

Step 3.2.3

Rewrite the expression.

$\frac{k (12 k^{2} + k + 12)}{3}$

Step 4

Apply the distributive property.

$\frac{k (12 k^{2}) + k \cdot k + k \cdot 12}{3}$

Step 5

Simplify.

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Step 5.1

Rewrite using the commutative property of multiplication.

$\frac{12 k \cdot k^{2} + k \cdot k + k \cdot 12}{3}$

Step 5.2

Multiply $k$ by $k$ .

$\frac{12 k \cdot k^{2} + k^{2} + k \cdot 12}{3}$

Step 5.3

Move $12$ to the left of $k$ .

$\frac{12 k \cdot k^{2} + k^{2} + 12 \cdot k}{3}$

Step 6

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

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Step 6.1

Move $k^{2}$ .

$\frac{12 (k^{2} k) + k^{2} + 12 \cdot k}{3}$

Step 6.2

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

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Step 6.2.1

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

$\frac{12 (k^{2} k^{1}) + k^{2} + 12 \cdot k}{3}$

Step 6.2.2

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

$\frac{12 k^{2 + 1} + k^{2} + 12 \cdot k}{3}$

Step 6.3

Add $2$ and $1$ .

$\frac{12 k^{3} + k^{2} + 12 \cdot k}{3}$

$\frac{12 k^{3} + k^{2} + 12 k}{3}$

Step 7

Split the fraction $\frac{12 k^{3} + k^{2} + 12 k}{3}$ into two fractions.

$\frac{12 k^{3} + k^{2}}{3} + \frac{12 k}{3}$

Step 8

Split the fraction $\frac{12 k^{3} + k^{2}}{3}$ into two fractions.

$\frac{12 k^{3}}{3} + \frac{k^{2}}{3} + \frac{12 k}{3}$

Step 9

Cancel the common factor of $12$ and $3$ .

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Step 9.1

Factor $3$ out of $12 k^{3}$ .

$\frac{3 (4 k^{3})}{3} + \frac{k^{2}}{3} + \frac{12 k}{3}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $3$ out of $3$ .

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

Step 9.2.2

Cancel the common factor.

$\frac{3 (4 k^{3})}{3 \cdot 1} + \frac{k^{2}}{3} + \frac{12 k}{3}$

Step 9.2.3

Rewrite the expression.

$\frac{4 k^{3}}{1} + \frac{k^{2}}{3} + \frac{12 k}{3}$

Step 9.2.4

Divide $4 k^{3}$ by $1$ .

$4 k^{3} + \frac{k^{2}}{3} + \frac{12 k}{3}$

Step 10

Cancel the common factor of $12$ and $3$ .

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Step 10.1

Factor $3$ out of $12 k$ .

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

Step 10.2

Cancel the common factors.

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Step 10.2.1

Factor $3$ out of $3$ .

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

Step 10.2.2

Cancel the common factor.

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

Step 10.2.3

Rewrite the expression.

$4 k^{3} + \frac{k^{2}}{3} + \frac{4 k}{1}$

Step 10.2.4

Divide $4 k$ by $1$ .

$4 k^{3} + \frac{k^{2}}{3} + 4 k$