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

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

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

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Reorder $2 a$ and $b (- a + 2)$ .

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

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

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

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

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

Simplify each term.

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Apply the distributive property.

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

Rewrite using the commutative property of multiplication.

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

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

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

Apply the distributive property.

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

Simplify.

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Multiply $- 1$ by $3$ .

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

Multiply $2$ by $3$ .

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

Multiply $2$ by $3$ .

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

Remove parentheses.

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

Add $a$ and $6 a$ .

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

Add $b$ and $6 b$ .

$- (7 a + 7 b - 3 b a)$

Factor.

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Factor $- 1$ out of $7 a + 7 b - 3 b a$ .

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Reorder the expression.

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Move $b$ .

$- (7 a + 7 b - 3 a b)$

Move $7 b$ .

$- (7 a - 3 a b + 7 b)$

Reorder $7 a$ and $- 3 a b$ .

$- (- 3 a b + 7 a + 7 b)$

Factor $- 1$ out of $- 3 a b$ .

$- (- (3 a b) + 7 a + 7 b)$

Factor $- 1$ out of $7 a$ .

$- (- (3 a b) - (- 7 a) + 7 b)$

Factor $- 1$ out of $7 b$ .

$- (- (3 a b) - (- 7 a) - (- 7 b))$

Factor $- 1$ out of $- (3 a b) - (- 7 a)$ .

$- (- (3 a b - 7 a) - (- 7 b))$

Factor $- 1$ out of $- (3 a b - 7 a) - (- 7 b)$ .

$- - (3 a b - 7 a - 7 b)$

Remove unnecessary parentheses.

$- - 1 (3 a b - 7 a - 7 b)$

Combine exponents.

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Factor out negative.

$- - (3 a b - 7 a - 7 b)$

Multiply $- 1$ by $- 1$ .

$1 (3 a b - 7 a - 7 b)$

Multiply $3 a b - 7 a - 7 b$ by $1$ .

$3 a b - 7 a - 7 b$

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

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