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

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

Evaluate

$$2y^{2}-10xy-7x^{2}$$

Solution Steps

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

$$-3x\left(2x+3y\right)-\left(x+2y\right)\left(x-y\right)$$

Use the distributive property to multiply -3x by 2x+3y.

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

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

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

Combine -xy and 2yx to get xy.

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

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

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

The opposite of -2y^{2} is 2y^{2}.

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

Combine -6x^{2} and -x^{2} to get -7x^{2}.

$$-7x^{2}-9xy-xy+2y^{2}$$

Combine -9xy and -xy to get -10xy.

$$-7x^{2}-10xy+2y^{2}$$

Expand

$$2y^{2}-10xy-7x^{2}$$

Solution Steps

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

$$-3x\left(2x+3y\right)-\left(x+2y\right)\left(x-y\right)$$

Use the distributive property to multiply -3x by 2x+3y.

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

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

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

Combine -xy and 2yx to get xy.

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

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

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

The opposite of -2y^{2} is 2y^{2}.

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

Combine -6x^{2} and -x^{2} to get -7x^{2}.

$$-7x^{2}-9xy-xy+2y^{2}$$

Combine -9xy and -xy to get -10xy.

$$-7x^{2}-10xy+2y^{2}$$