Solve 1+(2+x)y-(1+(-2-x)y)+3(1+xy)-3

$$1 + ( 2 + x ) y - ( 1 + ( - 2 - x ) y ) + 3 ( 1 + x y ) - 3$$

Evaluate

$$y\left(5x+4\right)$$

Solution Steps

Use the distributive property to multiply 2+x by y.

$$1+2y+xy-\left(1+\left(-2-x\right)y\right)+3\left(1+xy\right)-3$$

Use the distributive property to multiply -2-x by y.

$$1+2y+xy-\left(1-2y-xy\right)+3\left(1+xy\right)-3$$

To find the opposite of 1-2y-xy, find the opposite of each term.

$$1+2y+xy-1-\left(-2y\right)-\left(-xy\right)+3\left(1+xy\right)-3$$

Subtract 1 from 1 to get 0.

$$2y+xy-\left(-2y\right)-\left(-xy\right)+3\left(1+xy\right)-3$$

The opposite of -2y is 2y.

$$2y+xy+2y-\left(-xy\right)+3\left(1+xy\right)-3$$

Combine 2y and 2y to get 4y.

$$4y+xy-\left(-xy\right)+3\left(1+xy\right)-3$$

The opposite of -xy is xy.

$$4y+xy+xy+3\left(1+xy\right)-3$$

Combine xy and xy to get 2xy.

$$4y+2xy+3\left(1+xy\right)-3$$

Use the distributive property to multiply 3 by 1+xy.

$$4y+2xy+3+3xy-3$$

Combine 2xy and 3xy to get 5xy.

$$4y+5xy+3-3$$

Subtract 3 from 3 to get 0.

$$4y+5xy$$

Expand

$$5xy+4y$$

Solution Steps

Use the distributive property to multiply 2+x by y.

$$1+2y+xy-\left(1+\left(-2-x\right)y\right)+3\left(1+xy\right)-3$$

Use the distributive property to multiply -2-x by y.

$$1+2y+xy-\left(1-2y-xy\right)+3\left(1+xy\right)-3$$

To find the opposite of 1-2y-xy, find the opposite of each term.

$$1+2y+xy-1-\left(-2y\right)-\left(-xy\right)+3\left(1+xy\right)-3$$

Subtract 1 from 1 to get 0.

$$2y+xy-\left(-2y\right)-\left(-xy\right)+3\left(1+xy\right)-3$$

The opposite of -2y is 2y.

$$2y+xy+2y-\left(-xy\right)+3\left(1+xy\right)-3$$

Combine 2y and 2y to get 4y.

$$4y+xy-\left(-xy\right)+3\left(1+xy\right)-3$$

The opposite of -xy is xy.

$$4y+xy+xy+3\left(1+xy\right)-3$$

Combine xy and xy to get 2xy.

$$4y+2xy+3\left(1+xy\right)-3$$

Use the distributive property to multiply 3 by 1+xy.

$$4y+2xy+3+3xy-3$$

Combine 2xy and 3xy to get 5xy.

$$4y+5xy+3-3$$

Subtract 3 from 3 to get 0.

$$4y+5xy$$