Solve (x-2y)(x+3y)-(2x-y)(x-4y)

$$( x - 2 y ) ( x + 3 y ) - ( 2 x - y ) ( x - 4 y )$$

Evaluate

$$-x^{2}+10xy-10y^{2}$$

Solution Steps

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

$$x^{2}+3xy-2yx-6y^{2}-\left(2x-y\right)\left(x-4y\right)$$

Combine 3xy and -2yx to get xy.

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

Apply the distributive property by multiplying each term of 2x-y by each term of x-4y.

$$x^{2}+xy-6y^{2}-\left(2x^{2}-8xy-yx+4y^{2}\right)$$

Combine -8xy and -yx to get -9xy.

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

To find the opposite of 2x^{2}-9xy+4y^{2}, find the opposite of each term.

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

The opposite of -9xy is 9xy.

$$x^{2}+xy-6y^{2}-2x^{2}+9xy-4y^{2}$$

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

$$-x^{2}+xy-6y^{2}+9xy-4y^{2}$$

Combine xy and 9xy to get 10xy.

$$-x^{2}+10xy-6y^{2}-4y^{2}$$

Combine -6y^{2} and -4y^{2} to get -10y^{2}.

$$-x^{2}+10xy-10y^{2}$$

Expand

$$-x^{2}+10xy-10y^{2}$$

Solution Steps

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

$$x^{2}+3xy-2yx-6y^{2}-\left(2x-y\right)\left(x-4y\right)$$

Combine 3xy and -2yx to get xy.

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

Apply the distributive property by multiplying each term of 2x-y by each term of x-4y.

$$x^{2}+xy-6y^{2}-\left(2x^{2}-8xy-yx+4y^{2}\right)$$

Combine -8xy and -yx to get -9xy.

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

To find the opposite of 2x^{2}-9xy+4y^{2}, find the opposite of each term.

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

The opposite of -9xy is 9xy.

$$x^{2}+xy-6y^{2}-2x^{2}+9xy-4y^{2}$$

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

$$-x^{2}+xy-6y^{2}+9xy-4y^{2}$$

Combine xy and 9xy to get 10xy.

$$-x^{2}+10xy-6y^{2}-4y^{2}$$

Combine -6y^{2} and -4y^{2} to get -10y^{2}.

$$-x^{2}+10xy-10y^{2}$$