Solve xy-2x[2y-1/2(x+y)]

$$x y - 2 x [ 2 y - \frac { 1 } { 2 } ( x + y ) ]$$

Evaluate

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

Solution Steps

Use the distributive property to multiply -\frac{1}{2} by x+y.

$$xy-2x\left(2y-\frac{1}{2}x-\frac{1}{2}y\right)$$

Combine 2y and -\frac{1}{2}y to get \frac{3}{2}y.

$$xy-2x\left(\frac{3}{2}y-\frac{1}{2}x\right)$$

Use the distributive property to multiply -2x by \frac{3}{2}y-\frac{1}{2}x.

$$xy-2x\times \frac{3}{2}y-2x\left(-\frac{1}{2}\right)x$$

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

$$xy-2x\times \frac{3}{2}y-2x^{2}\left(-\frac{1}{2}\right)$$

Multiply -2 times \frac{3}{2}.

$$xy-3xy-2x^{2}\left(-\frac{1}{2}\right)$$

Multiply -2 times -\frac{1}{2}.

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

Combine xy and -3xy to get -2xy.

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

Expand

$$x^{2}-2xy$$

Solution Steps

Use the distributive property to multiply -\frac{1}{2} by x+y.

$$xy-2x\left(2y-\frac{1}{2}x-\frac{1}{2}y\right)$$

Combine 2y and -\frac{1}{2}y to get \frac{3}{2}y.

$$xy-2x\left(\frac{3}{2}y-\frac{1}{2}x\right)$$

Use the distributive property to multiply -2x by \frac{3}{2}y-\frac{1}{2}x.

$$xy-2x\times \frac{3}{2}y-2x\left(-\frac{1}{2}\right)x$$

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

$$xy-2x\times \frac{3}{2}y-2x^{2}\left(-\frac{1}{2}\right)$$

Multiply -2 times \frac{3}{2}.

$$xy-3xy-2x^{2}\left(-\frac{1}{2}\right)$$

Multiply -2 times -\frac{1}{2}.

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

Combine xy and -3xy to get -2xy.

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