Factor (1+3a)(x+1)-2a(x+1)+3(x+1)

$(1 + 3 a) (x + 1) - 2 a (x + 1) + 3 (x + 1)$

Factor $- (x + 1)$ out of $(1 + 3 a) (x + 1) - 2 a (x + 1) + 3 (x + 1)$ .

Reorder $1$ and $3 a$ .

$(3 a + 1) (x + 1) - 2 a (x + 1) + 3 (x + 1)$

Factor $- (x + 1)$ out of $(3 a + 1) (x + 1)$ .

$- (x + 1) (- 3 a - 1) - 2 a (x + 1) + 3 (x + 1)$

Factor $- (x + 1)$ out of $- 2 a (x + 1)$ .

$- (x + 1) (- 3 a - 1) - (x + 1) (2 a) + 3 (x + 1)$

Factor $- (x + 1)$ out of $3 (x + 1)$ .

$- (x + 1) (- 3 a - 1) - (x + 1) (2 a) - (x + 1) (- 3)$

Factor $- (x + 1)$ out of $- (x + 1) (- 3 a - 1) - (x + 1) (2 a)$ .

$- (x + 1) (- 3 a - 1 + 2 a) - (x + 1) (- 3)$

Factor $- (x + 1)$ out of $- (x + 1) (- 3 a - 1 + 2 a) - (x + 1) (- 3)$ .

$- (x + 1) (- 3 a - 1 + 2 a - 3)$

Regroup terms.

$- (x + 1) (- 3 a + 2 a - 1 - 3)$

Add $- 3 a$ and $2 a$ .

$- (x + 1) (- a - 1 - 3)$

Subtract $3$ from $- 1$ .

$- (x + 1) (- a - 4)$

Factor.

Factor $- 1$ out of $- a - 4$ .

Factor $- 1$ out of $- a$ .

$- (x + 1) (- (a) - 4)$

Rewrite $- 4$ as $- 1 (4)$ .

$- (x + 1) (- (a) - 1 (4))$

Factor $- 1$ out of $- (a) - 1 (4)$ .

$- (x + 1) (- (a + 4))$

Remove unnecessary parentheses.

$- (x + 1) \cdot - 1 (a + 4)$

Combine exponents.

Factor out negative.

$- ((x + 1) \cdot - 1 (a + 4))$

Multiply $- 1$ by $- 1$ .

$1 ((x + 1) (a + 4))$

Multiply $x + 1$ by $1$ .

$(x + 1) (a + 4)$