Solve -(x-1/2y)^2

$$- ( x - \frac { 1 } { 2 } y ) ^ { 2 }$$

Evaluate

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

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-\frac{1}{2}y\right)^{2}.

$$-\left(x^{2}-xy+\frac{1}{4}y^{2}\right)$$

To find the opposite of x^{2}-xy+\frac{1}{4}y^{2}, find the opposite of each term.

$$-x^{2}+xy-\frac{1}{4}y^{2}$$

Expand

$$xy-\frac{y^{2}}{4}-x^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-\frac{1}{2}y\right)^{2}.

$$-\left(x^{2}-xy+\frac{1}{4}y^{2}\right)$$

To find the opposite of x^{2}-xy+\frac{1}{4}y^{2}, find the opposite of each term.

$$-x^{2}+xy-\frac{1}{4}y^{2}$$