Algebra Examples

$3 n (n^{2} - 6 n + 5)$

Step 1

Apply the distributive property.

$3 n \cdot n^{2} + 3 n (- 6 n) + 3 n \cdot 5$

Step 2

Simplify.

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Step 2.1

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

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Step 2.1.1

Move $n^{2}$ .

$3 (n^{2} n) + 3 n (- 6 n) + 3 n \cdot 5$

Step 2.1.2

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

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Step 2.1.2.1

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

$3 (n^{2} n^{1}) + 3 n (- 6 n) + 3 n \cdot 5$

Step 2.1.2.2

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

$3 n^{2 + 1} + 3 n (- 6 n) + 3 n \cdot 5$

Step 2.1.3

Add $2$ and $1$ .

$3 n^{3} + 3 n (- 6 n) + 3 n \cdot 5$

Step 2.2

Rewrite using the commutative property of multiplication.

$3 n^{3} + 3 \cdot - 6 n \cdot n + 3 n \cdot 5$

Step 2.3

Multiply $5$ by $3$ .

$3 n^{3} + 3 \cdot - 6 n \cdot n + 15 n$

Step 3

Simplify each term.

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Step 3.1

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

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Step 3.1.1

Move $n$ .

$3 n^{3} + 3 \cdot - 6 (n \cdot n) + 15 n$

Step 3.1.2

Multiply $n$ by $n$ .

$3 n^{3} + 3 \cdot - 6 n^{2} + 15 n$

Step 3.2

Multiply $3$ by $- 6$ .

$3 n^{3} - 18 n^{2} + 15 n$