Solve (x-2y)(-x-2y)-2xleft(x-yright)

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

Evaluate

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

Solution Steps

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

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

Multiply -2 and -1 to get 2.

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

Combine -2xy and 2yx to get 0.

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

Multiply x and x to get x^{2}.

$$x^{2}\left(-1\right)+4y^{2}-2x\left(x-y\right)$$

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

$$x^{2}\left(-1\right)+4y^{2}-2x^{2}+2xy$$

Combine x^{2}\left(-1\right) and -2x^{2} to get -3x^{2}.

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

Expand

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

Solution Steps

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

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

Multiply -2 and -1 to get 2.

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

Combine -2xy and 2yx to get 0.

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

Multiply x and x to get x^{2}.

$$x^{2}\left(-1\right)+4y^{2}-2x\left(x-y\right)$$

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

$$x^{2}\left(-1\right)+4y^{2}-2x^{2}+2xy$$

Combine x^{2}\left(-1\right) and -2x^{2} to get -3x^{2}.

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