Simplify (2n+3)^2

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

Step 1

Rewrite ${(2 n + 3)}^{2}$ as $(2 n + 3) (2 n + 3)$ .

$(2 n + 3) (2 n + 3)$

Step 2

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

Apply the distributive property.

$2 n (2 n + 3) + 3 (2 n + 3)$

Apply the distributive property.

$2 n (2 n) + 2 n \cdot 3 + 3 (2 n + 3)$

Apply the distributive property.

$2 n (2 n) + 2 n \cdot 3 + 3 (2 n) + 3 \cdot 3$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 2 n \cdot n + 2 n \cdot 3 + 3 (2 n) + 3 \cdot 3$

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

Move $n$ .

$2 \cdot 2 (n \cdot n) + 2 n \cdot 3 + 3 (2 n) + 3 \cdot 3$

Multiply $n$ by $n$ .

$2 \cdot 2 n^{2} + 2 n \cdot 3 + 3 (2 n) + 3 \cdot 3$

Multiply $2$ by $2$ .

$4 n^{2} + 2 n \cdot 3 + 3 (2 n) + 3 \cdot 3$

Multiply $3$ by $2$ .

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

Multiply $2$ by $3$ .

$4 n^{2} + 6 n + 6 n + 3 \cdot 3$

Multiply $3$ by $3$ .

$4 n^{2} + 6 n + 6 n + 9$

Add $6 n$ and $6 n$ .

$4 n^{2} + 12 n + 9$