Algebra Examples

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

Step 1

Simplify by adding terms.

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Step 1.1

Remove parentheses.

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

Step 1.2

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

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Step 1.2.1

Subtract $a$ from $a$ .

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

Step 1.2.2

Subtract $b + a$ from $0$ .

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

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Multiply $- - a$ .

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Step 2.3.1

Multiply $- 1$ by $- 1$ .

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

Step 2.3.2

Multiply $a$ by $1$ .

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

Step 2.4

Multiply $2$ by $- 1$ .

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

Step 3

Simplify by adding terms.

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Step 3.1

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

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Step 3.1.1

Add $- b$ and $b$ .

$- a + 0 + a - 2 b$

Step 3.1.2

Add $- a$ and $0$ .

$- a + a - 2 b$

Step 3.1.3

Add $- a$ and $a$ .

$0 - 2 b$

Step 3.2

Subtract $2 b$ from $0$ .

$- 2 b$