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

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

Simplify by adding terms.

Remove parentheses.

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

Combine the opposite terms in $a - (b + a) - a + b - (- a + 2 b)$ .

Subtract $a$ from $a$ .

$0 - (b + a) + b - (- a + 2 b)$

Subtract $b + a$ from $0$ .

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

Simplify each term.

Apply the distributive property.

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

Apply the distributive property.

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

Multiply $- - a$ .

Multiply $- 1$ by $- 1$ .

$- b - a + b + 1 a - (2 b)$

Multiply $a$ by $1$ .

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

Multiply $2$ by $- 1$ .

$- b - a + b + a - 2 b$

Simplify by adding terms.

Combine the opposite terms in $- b - a + b + a - 2 b$ .

Add $- b$ and $b$ .

$- a + 0 + a - 2 b$

Add $- a$ and $0$ .

$- a + a - 2 b$

Add $- a$ and $a$ .

$0 - 2 b$

Subtract $2 b$ from $0$ .

$- 2 b$