Factor (x+2)(x-12)-(3x+4)(x+2)

$(x + 2) (x - 12) - (3 x + 4) (x + 2)$

Factor $x + 2$ out of $(x + 2) (x - 12) - (3 x + 4) (x + 2)$ .

Factor $x + 2$ out of $- (3 x + 4) (x + 2)$ .

$(x + 2) (x - 12) + (x + 2) (- (3 x + 4))$

Factor $x + 2$ out of $(x + 2) (x - 12) + (x + 2) (- (3 x + 4))$ .

$(x + 2) (x - 12 - (3 x + 4))$

Apply the distributive property.

$(x + 2) (x - 12 - (3 x) - 1 \cdot 4)$

Multiply $3$ by $- 1$ .

$(x + 2) (x - 12 - 3 x - 1 \cdot 4)$

Multiply $- 1$ by $4$ .

$(x + 2) (x - 12 - 3 x - 4)$

Subtract $3 x$ from $x$ .

$(x + 2) (- 2 x - 12 - 4)$

Subtract $4$ from $- 12$ .

$(x + 2) (- 2 x - 16)$

Factor.

Factor $2$ out of $- 2 x - 16$ .

Factor $2$ out of $- 2 x$ .

$(x + 2) (2 (- x) - 16)$

Factor $2$ out of $- 16$ .

$(x + 2) (2 (- x) + 2 (- 8))$

Factor $2$ out of $2 (- x) + 2 (- 8)$ .

$(x + 2) (2 (- x - 8))$

Remove unnecessary parentheses.

$(x + 2) \cdot 2 (- x - 8)$

Factor.

Factor $- 1$ out of $- x - 8$ .

Factor $- 1$ out of $- x$ .

$(x + 2) \cdot 2 (- (x) - 8)$

Rewrite $- 8$ as $- 1 (8)$ .

$(x + 2) \cdot 2 (- (x) - 1 (8))$

Factor $- 1$ out of $- (x) - 1 (8)$ .

$(x + 2) \cdot 2 (- (x + 8))$

Remove unnecessary parentheses.

$(x + 2) \cdot 2 \cdot - 1 (x + 8)$

Combine exponents.

Factor out negative.

$- ((x + 2) \cdot 2 (x + 8))$

Multiply $2$ by $- 1$ .

$- 2 ((x + 2) (x + 8))$

Remove unnecessary parentheses.

$- 2 (x + 2) (x + 8)$