Find the Product (-12-n)^2

${(- 12 - n)}^{2}$

Step 1

Rewrite ${(- 12 - n)}^{2}$ as $(- 12 - n) (- 12 - n)$ .

$(- 12 - n) (- 12 - n)$

Step 2

Expand $(- 12 - n) (- 12 - n)$ using the FOIL Method.

Apply the distributive property.

$- 12 (- 12 - n) - n (- 12 - n)$

Apply the distributive property.

$- 12 \cdot - 12 - 12 (- n) - n (- 12 - n)$

Apply the distributive property.

$- 12 \cdot - 12 - 12 (- n) - n \cdot - 12 - n (- n)$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $- 12$ by $- 12$ .

$144 - 12 (- n) - n \cdot - 12 - n (- n)$

Multiply $- 1$ by $- 12$ .

$144 + 12 n - n \cdot - 12 - n (- n)$

Multiply $- 12$ by $- 1$ .

$144 + 12 n + 12 n - n (- n)$

Rewrite using the commutative property of multiplication.

$144 + 12 n + 12 n - 1 \cdot - 1 n \cdot n$

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

Move $n$ .

$144 + 12 n + 12 n - 1 \cdot - 1 (n \cdot n)$

Multiply $n$ by $n$ .

$144 + 12 n + 12 n - 1 \cdot - 1 n^{2}$

Multiply $- 1$ by $- 1$ .

$144 + 12 n + 12 n + 1 n^{2}$

Multiply $n^{2}$ by $1$ .

$144 + 12 n + 12 n + n^{2}$

Add $12 n$ and $12 n$ .

$144 + 24 n + n^{2}$