Simplify a-(a-(b-(a-b)))

$a - (a - (b - (a - b)))$

Step 1

Simplify each term.

Simplify each term.

Simplify each term.

Apply the distributive property.

$a - (a - (b - a - - b))$

Multiply $- - b$ .

Multiply $- 1$ by $- 1$ .

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

Multiply $b$ by $1$ .

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

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

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

Add $b$ and $b$ .

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

Apply the distributive property.

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

Multiply $- - a$ .

Multiply $- 1$ by $- 1$ .

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

Multiply $a$ by $1$ .

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

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

Multiply $2$ by $- 1$ .

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

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

Add $a$ and $a$ .

$a - (2 a - 2 b)$

Apply the distributive property.

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

Multiply $2$ by $- 1$ .

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

Multiply $- 2$ by $- 1$ .

$a - 2 a + 2 b$

$a - 2 a + 2 b$

Step 2

Subtract $2 a$ from $a$ .

$- a + 2 b$

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