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

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

Evaluate

$$3x^{2}-4xy-y^{2}$$

Solution Steps

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

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

Combine -xy and -2yx to get -3xy.

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

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

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

Combine -2xy and yx to get -xy.

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

Combine 2x^{2} and x^{2} to get 3x^{2}.

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

Combine -3xy and -xy to get -4xy.

$$3x^{2}-4xy+y^{2}-2y^{2}$$

Combine y^{2} and -2y^{2} to get -y^{2}.

$$3x^{2}-4xy-y^{2}$$

Expand

$$3x^{2}-4xy-y^{2}$$

Solution Steps

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

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

Combine -xy and -2yx to get -3xy.

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

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

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

Combine -2xy and yx to get -xy.

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

Combine 2x^{2} and x^{2} to get 3x^{2}.

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

Combine -3xy and -xy to get -4xy.

$$3x^{2}-4xy+y^{2}-2y^{2}$$

Combine y^{2} and -2y^{2} to get -y^{2}.

$$3x^{2}-4xy-y^{2}$$