Factor (3n+1)(4n+1)+(n+2)(4n+1)

$(3 n + 1) (4 n + 1) + (n + 2) (4 n + 1)$

Step 1

Factor $4 n + 1$ out of $(3 n + 1) (4 n + 1) + (n + 2) (4 n + 1)$ .

Factor $4 n + 1$ out of $(3 n + 1) (4 n + 1)$ .

$(4 n + 1) (3 n + 1) + (n + 2) (4 n + 1)$

Factor $4 n + 1$ out of $(n + 2) (4 n + 1)$ .

$(4 n + 1) (3 n + 1) + (4 n + 1) (n + 2)$

Factor $4 n + 1$ out of $(4 n + 1) (3 n + 1) + (4 n + 1) (n + 2)$ .

$(4 n + 1) (3 n + 1 + n + 2)$

Step 2

Add $3 n$ and $n$ .

$(4 n + 1) (4 n + 1 + 2)$

Step 3

Add $1$ and $2$ .

$(4 n + 1) (4 n + 3)$