Simplify (n+(n+1))^2

${(n + (n + 1))}^{2}$

Simplify by adding terms.

Remove parentheses.

${(n + n + 1)}^{2}$

Add $n$ and $n$ .

${(2 n + 1)}^{2}$

Rewrite ${(2 n + 1)}^{2}$ as $(2 n + 1) (2 n + 1)$ .

$(2 n + 1) (2 n + 1)$

Expand $(2 n + 1) (2 n + 1)$ using the FOIL Method.

Apply the distributive property.

$2 n (2 n + 1) + 1 (2 n + 1)$

Apply the distributive property.

$2 n (2 n) + 2 n \cdot 1 + 1 (2 n + 1)$

Apply the distributive property.

$2 n (2 n) + 2 n \cdot 1 + 1 (2 n) + 1 \cdot 1$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 2 n \cdot n + 2 n \cdot 1 + 1 (2 n) + 1 \cdot 1$

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

Move $n$ .

$2 \cdot 2 (n \cdot n) + 2 n \cdot 1 + 1 (2 n) + 1 \cdot 1$

Multiply $n$ by $n$ .

$2 \cdot 2 n^{2} + 2 n \cdot 1 + 1 (2 n) + 1 \cdot 1$

Multiply $2$ by $2$ .

$4 n^{2} + 2 n \cdot 1 + 1 (2 n) + 1 \cdot 1$

Multiply $2$ by $1$ .

$4 n^{2} + 2 n + 1 (2 n) + 1 \cdot 1$

Multiply $2 n$ by $1$ .

$4 n^{2} + 2 n + 2 n + 1 \cdot 1$

Multiply $1$ by $1$ .

$4 n^{2} + 2 n + 2 n + 1$

Add $2 n$ and $2 n$ .

$4 n^{2} + 4 n + 1$