Solve (x-2y)^2-(x-y)(x-y)-2y^2

$$( x - 2 y ) ^ { 2 } - ( x - y ) ( x - y ) - 2 y ^ { 2 }$$

Evaluate

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

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

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

Combine 4y^{2} and -y^{2} to get 3y^{2}.

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

Combine 3y^{2} and -2y^{2} to get y^{2}.

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

Expand

$$y^{2}-2xy$$

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

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

Combine 4y^{2} and -y^{2} to get 3y^{2}.

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

Combine 3y^{2} and -2y^{2} to get y^{2}.

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