Evaluate Using the Given Value a_n=(2n-6)(2n+3) ; a_11

$a_{n} = (2 n - 6) (2 n + 3)$ ; $a_{11}$

Expand $(2 n - 6) (2 n + 3)$ using the FOIL Method.

Apply the distributive property.

$a_{n} = 2 n (2 n + 3) - 6 (2 n + 3)$

Apply the distributive property.

$a_{n} = 2 n (2 n) + 2 n \cdot 3 - 6 (2 n + 3)$

Apply the distributive property.

$a_{n} = 2 n (2 n) + 2 n \cdot 3 - 6 (2 n) - 6 \cdot 3$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$a_{n} = 2 \cdot 2 n \cdot n + 2 n \cdot 3 - 6 (2 n) - 6 \cdot 3$

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

Move $n$ .

$a_{n} = 2 \cdot 2 (n \cdot n) + 2 n \cdot 3 - 6 (2 n) - 6 \cdot 3$

Multiply $n$ by $n$ .

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

Multiply $2$ by $2$ .

$a_{n} = 4 n^{2} + 2 n \cdot 3 - 6 (2 n) - 6 \cdot 3$

Multiply $3$ by $2$ .

$a_{n} = 4 n^{2} + 6 n - 6 (2 n) - 6 \cdot 3$

Multiply $2$ by $- 6$ .

$a_{n} = 4 n^{2} + 6 n - 12 n - 6 \cdot 3$

Multiply $- 6$ by $3$ .

$a_{n} = 4 n^{2} + 6 n - 12 n - 18$

Subtract $12 n$ from $6 n$ .

$a_{n} = 4 n^{2} - 6 n - 18$