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

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

Evaluate

$$-2x^{2}+8xy-4y^{2}$$

Solution Steps

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

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

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

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

Apply the distributive property by multiplying each term of 3x-2y by each term of x-3y.

$$x^{2}-3xy+2y^{2}-\left(3x^{2}-9xy-2yx+6y^{2}\right)$$

Combine -9xy and -2yx to get -11xy.

$$x^{2}-3xy+2y^{2}-\left(3x^{2}-11xy+6y^{2}\right)$$

To find the opposite of 3x^{2}-11xy+6y^{2}, find the opposite of each term.

$$x^{2}-3xy+2y^{2}-3x^{2}-\left(-11xy\right)-6y^{2}$$

The opposite of -11xy is 11xy.

$$x^{2}-3xy+2y^{2}-3x^{2}+11xy-6y^{2}$$

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

$$-2x^{2}-3xy+2y^{2}+11xy-6y^{2}$$

Combine -3xy and 11xy to get 8xy.

$$-2x^{2}+8xy+2y^{2}-6y^{2}$$

Combine 2y^{2} and -6y^{2} to get -4y^{2}.

$$-2x^{2}+8xy-4y^{2}$$

Expand

$$-2x^{2}+8xy-4y^{2}$$

Solution Steps

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

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

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

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

Apply the distributive property by multiplying each term of 3x-2y by each term of x-3y.

$$x^{2}-3xy+2y^{2}-\left(3x^{2}-9xy-2yx+6y^{2}\right)$$

Combine -9xy and -2yx to get -11xy.

$$x^{2}-3xy+2y^{2}-\left(3x^{2}-11xy+6y^{2}\right)$$

To find the opposite of 3x^{2}-11xy+6y^{2}, find the opposite of each term.

$$x^{2}-3xy+2y^{2}-3x^{2}-\left(-11xy\right)-6y^{2}$$

The opposite of -11xy is 11xy.

$$x^{2}-3xy+2y^{2}-3x^{2}+11xy-6y^{2}$$

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

$$-2x^{2}-3xy+2y^{2}+11xy-6y^{2}$$

Combine -3xy and 11xy to get 8xy.

$$-2x^{2}+8xy+2y^{2}-6y^{2}$$

Combine 2y^{2} and -6y^{2} to get -4y^{2}.

$$-2x^{2}+8xy-4y^{2}$$