Solve -(x+y)+(-3x+y-(-2x+y-(x-y))+2x)

$$-(x+y)+(-3x+y-(-2x+y-(x-y))+2x)$$

Evaluate

$$x-2y$$

Solution Steps

To find the opposite of x+y, find the opposite of each term.

$$-x-y+-3x+y-\left(-2x+y-\left(x-y\right)\right)+2x$$

To find the opposite of x-y, find the opposite of each term.

$$-x-y+-3x+y-\left(-2x+y-x-\left(-y\right)\right)+2x$$

The opposite of -y is y.

$$-x-y+-3x+y-\left(-2x+y-x+y\right)+2x$$

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

$$-x-y+-3x+y-\left(-3x+y+y\right)+2x$$

Combine y and y to get 2y.

$$-x-y-3x+y-\left(-3x+2y\right)+2x$$

To find the opposite of -3x+2y, find the opposite of each term.

$$-x-y-3x+y-\left(-3x\right)-2y+2x$$

The opposite of -3x is 3x.

$$-x-y-3x+y+3x-2y+2x$$

Combine -3x and 3x to get 0.

$$-x-y+y-2y+2x$$

Combine y and -2y to get -y.

$$-x-y-y+2x$$

Combine -y and -y to get -2y.

$$-x-2y+2x$$

Combine -x and 2x to get x.

$$x-2y$$

Expand

$$x-2y$$

Solution Steps

To find the opposite of x+y, find the opposite of each term.

$$-x-y+-3x+y-\left(-2x+y-\left(x-y\right)\right)+2x$$

To find the opposite of x-y, find the opposite of each term.

$$-x-y+-3x+y-\left(-2x+y-x-\left(-y\right)\right)+2x$$

The opposite of -y is y.

$$-x-y+-3x+y-\left(-2x+y-x+y\right)+2x$$

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

$$-x-y+-3x+y-\left(-3x+y+y\right)+2x$$

Combine y and y to get 2y.

$$-x-y-3x+y-\left(-3x+2y\right)+2x$$

To find the opposite of -3x+2y, find the opposite of each term.

$$-x-y-3x+y-\left(-3x\right)-2y+2x$$

The opposite of -3x is 3x.

$$-x-y-3x+y+3x-2y+2x$$

Combine -3x and 3x to get 0.

$$-x-y+y-2y+2x$$

Combine y and -2y to get -y.

$$-x-y-y+2x$$

Combine -y and -y to get -2y.

$$-x-2y+2x$$

Combine -x and 2x to get x.

$$x-2y$$