What is a-(b+a)+(-a+b)-(-a+2b) ?

The solution to a-(b+a)+(-a+b)-(-a+2b) is -2b

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simplify a-(b+a)+(-a+b)-(-a+2b)

simplify

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

- 2 b

Solution steps

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

Apply rule:

a + (b + c) = a + b + c

- (b + a) + (- a + b) = - (b + a) - a + b

= a - (b + a) - a + b - (- a + 2 b)

Group like terms

= - (b + a) - (- a + 2 b) + a - a + b

Add similar elements:

a - a = 0

= - (b + a) - (- a + 2 b) + b

- (b + a) = - b - a

- (- a + 2 b) = a - 2 b

= - b - a + a - 2 b + b

Add similar elements:

- a + a = 0

= - b - 2 b + b

Add similar elements:

- b + b = 0

= - 2 b

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