Algebra Examples

$\frac{27 n^{4} - 9 n^{3} + 63 n^{2}}{9 n}$

Step 1

Factor $9 n^{2}$ out of $27 n^{4} - 9 n^{3} + 63 n^{2}$ .

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Step 1.1

Factor $9 n^{2}$ out of $27 n^{4}$ .

$\frac{9 n^{2} (3 n^{2}) - 9 n^{3} + 63 n^{2}}{9 n}$

Step 1.2

Factor $9 n^{2}$ out of $- 9 n^{3}$ .

$\frac{9 n^{2} (3 n^{2}) + 9 n^{2} (- n) + 63 n^{2}}{9 n}$

Step 1.3

Factor $9 n^{2}$ out of $63 n^{2}$ .

$\frac{9 n^{2} (3 n^{2}) + 9 n^{2} (- n) + 9 n^{2} (7)}{9 n}$

Step 1.4

Factor $9 n^{2}$ out of $9 n^{2} (3 n^{2}) + 9 n^{2} (- n)$ .

$\frac{9 n^{2} (3 n^{2} - n) + 9 n^{2} (7)}{9 n}$

Step 1.5

Factor $9 n^{2}$ out of $9 n^{2} (3 n^{2} - n) + 9 n^{2} (7)$ .

$\frac{9 n^{2} (3 n^{2} - n + 7)}{9 n}$

Step 2

Cancel the common factor of $9$ .

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Step 2.1

Cancel the common factor.

$\frac{9 n^{2} (3 n^{2} - n + 7)}{9 n}$

Step 2.2

Rewrite the expression.

$\frac{n^{2} (3 n^{2} - n + 7)}{n}$

Step 3

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

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Step 3.1

Factor $n$ out of $n^{2} (3 n^{2} - n + 7)$ .

$\frac{n (n (3 n^{2} - n + 7))}{n}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

$\frac{n (n (3 n^{2} - n + 7))}{n^{1}}$

Step 3.2.2

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

$\frac{n (n (3 n^{2} - n + 7))}{n \cdot 1}$

Step 3.2.3

Cancel the common factor.

$\frac{n (n (3 n^{2} - n + 7))}{n \cdot 1}$

Step 3.2.4

Rewrite the expression.

$\frac{n (3 n^{2} - n + 7)}{1}$

Step 3.2.5

Divide $n (3 n^{2} - n + 7)$ by $1$ .

$n (3 n^{2} - n + 7)$

Step 4

Apply the distributive property.

$n (3 n^{2}) + n (- n) + n \cdot 7$

Step 5

Simplify.

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Step 5.1

Rewrite using the commutative property of multiplication.

$3 n \cdot n^{2} + n (- n) + n \cdot 7$

Step 5.2

Rewrite using the commutative property of multiplication.

$3 n \cdot n^{2} - n \cdot n + n \cdot 7$

Step 5.3

Move $7$ to the left of $n$ .

$3 n \cdot n^{2} - n \cdot n + 7 \cdot n$

Step 6

Simplify each term.

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Step 6.1

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

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Step 6.1.1

Move $n^{2}$ .

$3 (n^{2} n) - n \cdot n + 7 \cdot n$

Step 6.1.2

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

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Step 6.1.2.1

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

$3 (n^{2} n^{1}) - n \cdot n + 7 \cdot n$

Step 6.1.2.2

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

$3 n^{2 + 1} - n \cdot n + 7 \cdot n$

Step 6.1.3

Add $2$ and $1$ .

$3 n^{3} - n \cdot n + 7 \cdot n$

Step 6.2

Multiply $n$ by $n$ by adding the exponents.

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Step 6.2.1

Move $n$ .

$3 n^{3} - (n \cdot n) + 7 \cdot n$

Step 6.2.2

Multiply $n$ by $n$ .

$3 n^{3} - n^{2} + 7 \cdot n$

$3 n^{3} - n^{2} + 7 n$