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

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

Evaluate

$$\left(3x-y\right)\left(3y-5x\right)$$

Solution Steps

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

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

Combine 3xy and 6yx to get 9xy.

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

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

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

Combine -2xy and -3yx to get -5xy.

$$9xy-9x^{2}-2y^{2}-\left(6x^{2}-5xy+y^{2}\right)$$

To find the opposite of 6x^{2}-5xy+y^{2}, find the opposite of each term.

$$9xy-9x^{2}-2y^{2}-6x^{2}-\left(-5xy\right)-y^{2}$$

The opposite of -5xy is 5xy.

$$9xy-9x^{2}-2y^{2}-6x^{2}+5xy-y^{2}$$

Combine -9x^{2} and -6x^{2} to get -15x^{2}.

$$9xy-15x^{2}-2y^{2}+5xy-y^{2}$$

Combine 9xy and 5xy to get 14xy.

$$14xy-15x^{2}-2y^{2}-y^{2}$$

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

$$14xy-15x^{2}-3y^{2}$$

Expand

$$-15x^{2}+14xy-3y^{2}$$

Solution Steps

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

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

Combine 3xy and 6yx to get 9xy.

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

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

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

Combine -2xy and -3yx to get -5xy.

$$9xy-9x^{2}-2y^{2}-\left(6x^{2}-5xy+y^{2}\right)$$

To find the opposite of 6x^{2}-5xy+y^{2}, find the opposite of each term.

$$9xy-9x^{2}-2y^{2}-6x^{2}-\left(-5xy\right)-y^{2}$$

The opposite of -5xy is 5xy.

$$9xy-9x^{2}-2y^{2}-6x^{2}+5xy-y^{2}$$

Combine -9x^{2} and -6x^{2} to get -15x^{2}.

$$9xy-15x^{2}-2y^{2}+5xy-y^{2}$$

Combine 9xy and 5xy to get 14xy.

$$14xy-15x^{2}-2y^{2}-y^{2}$$

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

$$14xy-15x^{2}-3y^{2}$$