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

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

Evaluate

$$2y\left(3+2y-4x\right)$$

Solution Steps

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

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

Combine -2xy and -2yx to get -4xy.

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

Use the distributive property to multiply x by x+4y-3.

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

To find the opposite of x^{2}+4xy-3x, find the opposite of each term.

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

The opposite of -3x is 3x.

$$x^{2}-4xy-3x+4y^{2}+6y-x^{2}-4xy+3x$$

Combine x^{2} and -x^{2} to get 0.

$$-4xy-3x+4y^{2}+6y-4xy+3x$$

Combine -4xy and -4xy to get -8xy.

$$-8xy-3x+4y^{2}+6y+3x$$

Combine -3x and 3x to get 0.

$$-8xy+4y^{2}+6y$$

Expand

$$6y+4y^{2}-8xy$$

Solution Steps

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

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

Combine -2xy and -2yx to get -4xy.

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

Use the distributive property to multiply x by x+4y-3.

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

To find the opposite of x^{2}+4xy-3x, find the opposite of each term.

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

The opposite of -3x is 3x.

$$x^{2}-4xy-3x+4y^{2}+6y-x^{2}-4xy+3x$$

Combine x^{2} and -x^{2} to get 0.

$$-4xy-3x+4y^{2}+6y-4xy+3x$$

Combine -4xy and -4xy to get -8xy.

$$-8xy-3x+4y^{2}+6y+3x$$

Combine -3x and 3x to get 0.

$$-8xy+4y^{2}+6y$$