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

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

Evaluate

$$2y^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of x+2y by each term of x+y.

$$x^{2}+xy+2yx+2y^{2}-x\left(x+3y\right)$$

Combine xy and 2yx to get 3xy.

$$x^{2}+3xy+2y^{2}-x\left(x+3y\right)$$

Use the distributive property to multiply x by x+3y.

$$x^{2}+3xy+2y^{2}-\left(x^{2}+3xy\right)$$

To find the opposite of x^{2}+3xy, find the opposite of each term.

$$x^{2}+3xy+2y^{2}-x^{2}-3xy$$

Combine x^{2} and -x^{2} to get 0.

$$3xy+2y^{2}-3xy$$

Combine 3xy and -3xy to get 0.

$$2y^{2}$$

Expand

$$2y^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of x+2y by each term of x+y.

$$x^{2}+xy+2yx+2y^{2}-x\left(x+3y\right)$$

Combine xy and 2yx to get 3xy.

$$x^{2}+3xy+2y^{2}-x\left(x+3y\right)$$

Use the distributive property to multiply x by x+3y.

$$x^{2}+3xy+2y^{2}-\left(x^{2}+3xy\right)$$

To find the opposite of x^{2}+3xy, find the opposite of each term.

$$x^{2}+3xy+2y^{2}-x^{2}-3xy$$

Combine x^{2} and -x^{2} to get 0.

$$3xy+2y^{2}-3xy$$

Combine 3xy and -3xy to get 0.

$$2y^{2}$$