Basic Math Examples

$(n - 1) (n^{2} + n + 2)$

Step 1

Expand $(n - 1) (n^{2} + n + 2)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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Step 2.1.1.1

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

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Step 2.1.1.1.1

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

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

Step 2.1.1.1.2

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

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

Step 2.1.1.2

Add $1$ and $2$ .

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

Step 2.1.2

Multiply $n$ by $n$ .

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

Step 2.1.3

Move $2$ to the left of $n$ .

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

Step 2.1.4

Rewrite $- 1 n^{2}$ as $- n^{2}$ .

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

Step 2.1.5

Rewrite $- 1 n$ as $- n$ .

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

Step 2.1.6

Multiply $- 1$ by $2$ .

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

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Combine the opposite terms in $n^{3} + n^{2} + 2 n - n^{2} - n - 2$ .

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Step 2.2.1.1

Subtract $n^{2}$ from $n^{2}$ .

$n^{3} + 2 n + 0 - n - 2$

Step 2.2.1.2

Add $n^{3} + 2 n$ and $0$ .

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

Step 2.2.2

Subtract $n$ from $2 n$ .

$n^{3} + n - 2$