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

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

Evaluate

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Solution Steps

Multiply x-2y and -2y+x to get \left(x-2y\right)^{2}.

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

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-2y\right)^{2}.

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

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

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

Multiply -2 and -1 to get 2.

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

Combine 2xy and 2yx to get 4xy.

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

Combine -4xy and 4xy to get 0.

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

Combine 4y^{2} and -4y^{2} to get 0.

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

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

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

Combine x^{2} and x^{2}\left(-1\right) to get 0.

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Factor

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Solution Steps

Factor out common term x-2y by using distributive property.

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

Consider -2y+x-x+2y. Simplify.

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