Factor (m+2)^2-(m+2)+mn*(n+2)+2n(n+2)

${(m + 2)}^{2} - (m + 2) + m n \cdot (n + 2) + 2 n (n + 2)$

Regroup terms.

${(m + 2)}^{2} - (m + 2) + m n \cdot (n + 2) + 2 n (n + 2)$

Factor $m + 2$ out of ${(m + 2)}^{2} - (m + 2)$ .

Factor $m + 2$ out of ${(m + 2)}^{2}$ .

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

Factor $m + 2$ out of $- (m + 2)$ .

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

Factor $m + 2$ out of $(m + 2) (m + 2) + (m + 2) \cdot - 1$ .

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

Subtract $1$ from $2$ .

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

Factor $n (n + 2)$ out of $m n \cdot (n + 2) + 2 n (n + 2)$ .

Factor $n (n + 2)$ out of $m n \cdot (n + 2)$ .

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

Factor $n (n + 2)$ out of $2 n (n + 2)$ .

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

Factor $n (n + 2)$ out of $n (n + 2) (m) + n (n + 2) (2)$ .

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

Factor $m + 2$ out of $(m + 2) (m + 1) + n (n + 2) (m + 2)$ .

Factor $m + 2$ out of $n (n + 2) (m + 2)$ .

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

Factor $m + 2$ out of $(m + 2) (m + 1) + (m + 2) (n (n + 2))$ .

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

Apply the distributive property.

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

Multiply $n$ by $n$ .

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

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

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