Solve 1/2x^2-(3x^2-xy+3y^2)-{left(3/2right)}^2y

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

Evaluate

$$xy-\frac{5x^{2}}{2}-3y^{2}-\frac{9y}{4}$$

Solution Steps

To find the opposite of 3x^{2}-xy+3y^{2}, find the opposite of each term.

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

Combine \frac{1}{2}x^{2} and -3x^{2} to get -\frac{5}{2}x^{2}.

$$-\frac{5}{2}x^{2}+xy-3y^{2}-\left(\frac{3}{2}\right)^{2}y$$

Calculate \frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$-\frac{5}{2}x^{2}+xy-3y^{2}-\frac{9}{4}y$$

Expand

$$xy-\frac{5x^{2}}{2}-3y^{2}-\frac{9y}{4}$$

Solution Steps

To find the opposite of 3x^{2}-xy+3y^{2}, find the opposite of each term.

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

Combine \frac{1}{2}x^{2} and -3x^{2} to get -\frac{5}{2}x^{2}.

$$-\frac{5}{2}x^{2}+xy-3y^{2}-\left(\frac{3}{2}\right)^{2}y$$

Calculate \frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$-\frac{5}{2}x^{2}+xy-3y^{2}-\frac{9}{4}y$$