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

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

Evaluate

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

Solution Steps

To find the opposite of x-2y, find the opposite of each term.

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

The opposite of -2y is 2y.

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

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

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

Multiply -1 and -1 to get 1.

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

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

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

Multiply 2 and -1 to get -2.

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

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

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

Expand

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

Solution Steps

To find the opposite of x-2y, find the opposite of each term.

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

The opposite of -2y is 2y.

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

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

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

Multiply -1 and -1 to get 1.

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

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

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

Multiply 2 and -1 to get -2.

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

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

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