Algebra Examples

$(16 n^{5} + 4 n^{4} + 2 n^{3}) \div 8 n$

Step 1

Rewrite the division as a fraction.

$\frac{16 n^{5} + 4 n^{4} + 2 n^{3}}{8 n}$

Step 2

Factor $2 n^{3}$ out of $16 n^{5} + 4 n^{4} + 2 n^{3}$ .

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Step 2.1

Factor $2 n^{3}$ out of $16 n^{5}$ .

$\frac{2 n^{3} (8 n^{2}) + 4 n^{4} + 2 n^{3}}{8 n}$

Step 2.2

Factor $2 n^{3}$ out of $4 n^{4}$ .

$\frac{2 n^{3} (8 n^{2}) + 2 n^{3} (2 n) + 2 n^{3}}{8 n}$

Step 2.3

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

$\frac{2 n^{3} (8 n^{2}) + 2 n^{3} (2 n) + 2 n^{3} (1)}{8 n}$

Step 2.4

Factor $2 n^{3}$ out of $2 n^{3} (8 n^{2}) + 2 n^{3} (2 n)$ .

$\frac{2 n^{3} (8 n^{2} + 2 n) + 2 n^{3} (1)}{8 n}$

Step 2.5

Factor $2 n^{3}$ out of $2 n^{3} (8 n^{2} + 2 n) + 2 n^{3} (1)$ .

$\frac{2 n^{3} (8 n^{2} + 2 n + 1)}{8 n}$

Step 3

Cancel the common factor of $2$ and $8$ .

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Step 3.1

Factor $2$ out of $2 n^{3} (8 n^{2} + 2 n + 1)$ .

$\frac{2 (n^{3} (8 n^{2} + 2 n + 1))}{8 n}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $8 n$ .

$\frac{2 (n^{3} (8 n^{2} + 2 n + 1))}{2 (4 n)}$

Step 3.2.2

Cancel the common factor.

$\frac{2 (n^{3} (8 n^{2} + 2 n + 1))}{2 (4 n)}$

Step 3.2.3

Rewrite the expression.

$\frac{n^{3} (8 n^{2} + 2 n + 1)}{4 n}$

Step 4

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

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Step 4.1

Factor $n$ out of $n^{3} (8 n^{2} + 2 n + 1)$ .

$\frac{n (n^{2} (8 n^{2} + 2 n + 1))}{4 n}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $n$ out of $4 n$ .

$\frac{n (n^{2} (8 n^{2} + 2 n + 1))}{n \cdot 4}$

Step 4.2.2

Cancel the common factor.

$\frac{n (n^{2} (8 n^{2} + 2 n + 1))}{n \cdot 4}$

Step 4.2.3

Rewrite the expression.

$\frac{n^{2} (8 n^{2} + 2 n + 1)}{4}$

Step 5

Apply the distributive property.

$\frac{n^{2} (8 n^{2}) + n^{2} (2 n) + n^{2} \cdot 1}{4}$

Step 6

Simplify.

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Step 6.1

Rewrite using the commutative property of multiplication.

$\frac{8 n^{2} n^{2} + n^{2} (2 n) + n^{2} \cdot 1}{4}$

Step 6.2

Rewrite using the commutative property of multiplication.

$\frac{8 n^{2} n^{2} + 2 n^{2} n + n^{2} \cdot 1}{4}$

Step 6.3

Multiply $n^{2}$ by $1$ .

$\frac{8 n^{2} n^{2} + 2 n^{2} n + n^{2}}{4}$

Step 7

Simplify each term.

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Step 7.1

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

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Step 7.1.1

Move $n^{2}$ .

$\frac{8 (n^{2} n^{2}) + 2 n^{2} n + n^{2}}{4}$

Step 7.1.2

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

$\frac{8 n^{2 + 2} + 2 n^{2} n + n^{2}}{4}$

Step 7.1.3

Add $2$ and $2$ .

$\frac{8 n^{4} + 2 n^{2} n + n^{2}}{4}$

Step 7.2

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

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Step 7.2.1

Move $n$ .

$\frac{8 n^{4} + 2 (n \cdot n^{2}) + n^{2}}{4}$

Step 7.2.2

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

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Step 7.2.2.1

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

$\frac{8 n^{4} + 2 (n^{1} n^{2}) + n^{2}}{4}$

Step 7.2.2.2

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

$\frac{8 n^{4} + 2 n^{1 + 2} + n^{2}}{4}$

Step 7.2.3

Add $1$ and $2$ .

$\frac{8 n^{4} + 2 n^{3} + n^{2}}{4}$

Step 8

Split the fraction $\frac{8 n^{4} + 2 n^{3} + n^{2}}{4}$ into two fractions.

$\frac{8 n^{4} + 2 n^{3}}{4} + \frac{n^{2}}{4}$

Step 9

Split the fraction $\frac{8 n^{4} + 2 n^{3}}{4}$ into two fractions.

$\frac{8 n^{4}}{4} + \frac{2 n^{3}}{4} + \frac{n^{2}}{4}$

Step 10

Cancel the common factor of $8$ and $4$ .

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Step 10.1

Factor $4$ out of $8 n^{4}$ .

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

Step 10.2

Cancel the common factors.

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Step 10.2.1

Factor $4$ out of $4$ .

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

Step 10.2.2

Cancel the common factor.

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

Step 10.2.3

Rewrite the expression.

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

Step 10.2.4

Divide $2 n^{4}$ by $1$ .

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

Step 11

Cancel the common factor of $2$ and $4$ .

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Step 11.1

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

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

Step 11.2

Cancel the common factors.

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Step 11.2.1

Factor $2$ out of $4$ .

$2 n^{4} + \frac{2 n^{3}}{2 \cdot 2} + \frac{n^{2}}{4}$

Step 11.2.2

Cancel the common factor.

$2 n^{4} + \frac{2 n^{3}}{2 \cdot 2} + \frac{n^{2}}{4}$

Step 11.2.3

Rewrite the expression.

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