Solve (x-y)-(x-y)^2+2y(x-3y)]div(-4y)

$$( x - y ) - ( x - y ) ^ { 2 } + 2 y ( x - 3 y ) ] \div ( - 4 y )$$

Evaluate

$$-x^{2}+4xy+x-7y^{2}-y$$

Solution Steps

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

$$x-y-\left(x^{2}-2xy+y^{2}\right)+2y\left(x-3y\right)$$

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

$$x-y-x^{2}+2xy-y^{2}+2y\left(x-3y\right)$$

Use the distributive property to multiply 2y by x-3y.

$$x-y-x^{2}+2xy-y^{2}+2yx-6y^{2}$$

Combine 2xy and 2yx to get 4xy.

$$x-y-x^{2}+4xy-y^{2}-6y^{2}$$

Combine -y^{2} and -6y^{2} to get -7y^{2}.

$$x-y-x^{2}+4xy-7y^{2}$$

Expand

$$-x^{2}+4xy+x-7y^{2}-y$$

Solution Steps

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

$$x-y-\left(x^{2}-2xy+y^{2}\right)+2y\left(x-3y\right)$$

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

$$x-y-x^{2}+2xy-y^{2}+2y\left(x-3y\right)$$

Use the distributive property to multiply 2y by x-3y.

$$x-y-x^{2}+2xy-y^{2}+2yx-6y^{2}$$

Combine 2xy and 2yx to get 4xy.

$$x-y-x^{2}+4xy-y^{2}-6y^{2}$$

Combine -y^{2} and -6y^{2} to get -7y^{2}.

$$x-y-x^{2}+4xy-7y^{2}$$