Simplify -(a+b)-3(2a+b(-a+2))

$- (a + b) - 3 (2 a + b (- a + 2))$

Simplify each term.

Apply the distributive property.

$- a - b - 3 (2 a + b (- a + 2))$

Simplify each term.

Apply the distributive property.

$- a - b - 3 (2 a + b (- a) + b \cdot 2)$

Rewrite using the commutative property of multiplication.

$- a - b - 3 (2 a - b a + b \cdot 2)$

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

$- a - b - 3 (2 a - b a + 2 b)$

Apply the distributive property.

$- a - b - 3 (2 a) - 3 (- b a) - 3 (2 b)$

Simplify.

Multiply $2$ by $- 3$ .

$- a - b - 6 a - 3 (- b a) - 3 (2 b)$

Multiply $- 1$ by $- 3$ .

$- a - b - 6 a + 3 (b a) - 3 (2 b)$

Multiply $2$ by $- 3$ .

$- a - b - 6 a + 3 (b a) - 6 b$

$- a - b - 6 a + 3 b a - 6 b$

Simplify by adding terms.

Subtract $6 a$ from $- a$ .

$- 7 a - b + 3 b a - 6 b$

Subtract $6 b$ from $- b$ .

$- 7 a - 7 b + 3 b a$