Solve -(a+b)+[-3a+b-{-2a+b-(a-b)}+2a]

$$- ( a + b ) + [ - 3 a + b - \{ - 2 a + b - ( a - b ) \} + 2 a ]$$

Evaluate

$$a-2b$$

Solution Steps

To find the opposite of a+b, find the opposite of each term.

$$-a-b+-3a+b-\left(-2a+b-\left(a-b\right)\right)+2a$$

To find the opposite of a-b, find the opposite of each term.

$$-a-b+-3a+b-\left(-2a+b-a-\left(-b\right)\right)+2a$$

The opposite of -b is b.

$$-a-b+-3a+b-\left(-2a+b-a+b\right)+2a$$

Combine -2a and -a to get -3a.

$$-a-b+-3a+b-\left(-3a+b+b\right)+2a$$

Combine b and b to get 2b.

$$-a-b-3a+b-\left(-3a+2b\right)+2a$$

To find the opposite of -3a+2b, find the opposite of each term.

$$-a-b-3a+b-\left(-3a\right)-2b+2a$$

The opposite of -3a is 3a.

$$-a-b-3a+b+3a-2b+2a$$

Combine -3a and 3a to get 0.

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

Combine b and -2b to get -b.

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

Combine -b and -b to get -2b.

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

Combine -a and 2a to get a.

$$a-2b$$

Expand

$$a-2b$$

Solution Steps

To find the opposite of a+b, find the opposite of each term.

$$-a-b+-3a+b-\left(-2a+b-\left(a-b\right)\right)+2a$$

To find the opposite of a-b, find the opposite of each term.

$$-a-b+-3a+b-\left(-2a+b-a-\left(-b\right)\right)+2a$$

The opposite of -b is b.

$$-a-b+-3a+b-\left(-2a+b-a+b\right)+2a$$

Combine -2a and -a to get -3a.

$$-a-b+-3a+b-\left(-3a+b+b\right)+2a$$

Combine b and b to get 2b.

$$-a-b-3a+b-\left(-3a+2b\right)+2a$$

To find the opposite of -3a+2b, find the opposite of each term.

$$-a-b-3a+b-\left(-3a\right)-2b+2a$$

The opposite of -3a is 3a.

$$-a-b-3a+b+3a-2b+2a$$

Combine -3a and 3a to get 0.

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

Combine b and -2b to get -b.

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

Combine -b and -b to get -2b.

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

Combine -a and 2a to get a.

$$a-2b$$