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

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

Evaluate

$$y\left(6y-5x\right)$$

Solution Steps

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

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

Use the distributive property to multiply x+2y by x-y and combine like terms.

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

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

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

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

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

Combine -4xy and -xy to get -5xy.

$$-5xy+4y^{2}+2y^{2}$$

Combine 4y^{2} and 2y^{2} to get 6y^{2}.

$$-5xy+6y^{2}$$

Expand

$$6y^{2}-5xy$$

Solution Steps

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

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

Use the distributive property to multiply x+2y by x-y and combine like terms.

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

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

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

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

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

Combine -4xy and -xy to get -5xy.

$$-5xy+4y^{2}+2y^{2}$$

Combine 4y^{2} and 2y^{2} to get 6y^{2}.

$$-5xy+6y^{2}$$