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

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

Evaluate

$$-5x^{2}+12xy-12y^{2}$$

Solution Steps

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

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

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

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

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

$$x^{2}-xy-6y^{2}-\left(6x^{2}-4xy-9yx+6y^{2}\right)$$

Combine -4xy and -9yx to get -13xy.

$$x^{2}-xy-6y^{2}-\left(6x^{2}-13xy+6y^{2}\right)$$

To find the opposite of 6x^{2}-13xy+6y^{2}, find the opposite of each term.

$$x^{2}-xy-6y^{2}-6x^{2}-\left(-13xy\right)-6y^{2}$$

The opposite of -13xy is 13xy.

$$x^{2}-xy-6y^{2}-6x^{2}+13xy-6y^{2}$$

Combine x^{2} and -6x^{2} to get -5x^{2}.

$$-5x^{2}-xy-6y^{2}+13xy-6y^{2}$$

Combine -xy and 13xy to get 12xy.

$$-5x^{2}+12xy-6y^{2}-6y^{2}$$

Combine -6y^{2} and -6y^{2} to get -12y^{2}.

$$-5x^{2}+12xy-12y^{2}$$

Expand

$$-5x^{2}+12xy-12y^{2}$$

Solution Steps

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

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

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

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

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

$$x^{2}-xy-6y^{2}-\left(6x^{2}-4xy-9yx+6y^{2}\right)$$

Combine -4xy and -9yx to get -13xy.

$$x^{2}-xy-6y^{2}-\left(6x^{2}-13xy+6y^{2}\right)$$

To find the opposite of 6x^{2}-13xy+6y^{2}, find the opposite of each term.

$$x^{2}-xy-6y^{2}-6x^{2}-\left(-13xy\right)-6y^{2}$$

The opposite of -13xy is 13xy.

$$x^{2}-xy-6y^{2}-6x^{2}+13xy-6y^{2}$$

Combine x^{2} and -6x^{2} to get -5x^{2}.

$$-5x^{2}-xy-6y^{2}+13xy-6y^{2}$$

Combine -xy and 13xy to get 12xy.

$$-5x^{2}+12xy-6y^{2}-6y^{2}$$

Combine -6y^{2} and -6y^{2} to get -12y^{2}.

$$-5x^{2}+12xy-12y^{2}$$