Simplify (n+2)^5(n+2)^-3

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

Step 1

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

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

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

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.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 4

Simplify and combine like terms.

Simplify each term.

Multiply $n$ by $n$ .

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

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

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

Multiply $2$ by $2$ .

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

Add $2 n$ and $2 n$ .

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