Algebra Examples

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

Step 1

Multiply ${(n + 2)}^{5}$ by ${(n + 2)}^{- 3}$ by adding the exponents.

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Step 1.1

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

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

Step 1.2

Subtract $3$ from $5$ .

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

Step 2

Rewrite ${(n + 2)}^{2}$ as $(n + 2) (n + 2)$ .

$(n + 2) (n + 2)$

Step 3

Expand $(n + 2) (n + 2)$ using the FOIL Method.

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Step 3.1

Apply the distributive property.

$n (n + 2) + 2 (n + 2)$

Step 3.2

Apply the distributive property.

$n \cdot n + n \cdot 2 + 2 (n + 2)$

Step 3.3

Apply the distributive property.

$n \cdot n + n \cdot 2 + 2 n + 2 \cdot 2$

Step 4

Simplify and combine like terms.

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Step 4.1

Simplify each term.

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Step 4.1.1

Multiply $n$ by $n$ .

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

Step 4.1.2

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

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

Step 4.1.3

Multiply $2$ by $2$ .

$n^{2} + 2 n + 2 n + 4$

Step 4.2

Add $2 n$ and $2 n$ .

$n^{2} + 4 n + 4$