Solve -6xy+(1/2x-y)(y-1/2x)+5x(y+1)-(-x^2-y^2)=

$$-6xy+( \frac{ 1 }{ 2 } x-y)(y- \frac{ 1 }{ 2 } x)+5x(y+1)-(- { x }^{ 2 } - { y }^{ 2 } )=$$

Evaluate

$$\frac{3x^{2}}{4}+5x$$

Solution Steps

Use the distributive property to multiply \frac{1}{2}x-y by y-\frac{1}{2}x and combine like terms.

$$-6xy+xy-\frac{1}{4}x^{2}-y^{2}+5x\left(y+1\right)-\left(-x^{2}-y^{2}\right)$$

Combine -6xy and xy to get -5xy.

$$-5xy-\frac{1}{4}x^{2}-y^{2}+5x\left(y+1\right)-\left(-x^{2}-y^{2}\right)$$

Use the distributive property to multiply 5x by y+1.

$$-5xy-\frac{1}{4}x^{2}-y^{2}+5xy+5x-\left(-x^{2}-y^{2}\right)$$

Combine -5xy and 5xy to get 0.

$$-\frac{1}{4}x^{2}-y^{2}+5x-\left(-x^{2}-y^{2}\right)$$

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

$$-\frac{1}{4}x^{2}-y^{2}+5x-\left(-x^{2}\right)+y^{2}$$

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

$$-\frac{1}{4}x^{2}+5x-\left(-x^{2}\right)$$

Multiply -1 and -1 to get 1.

$$-\frac{1}{4}x^{2}+5x+x^{2}$$

Combine -\frac{1}{4}x^{2} and x^{2} to get \frac{3}{4}x^{2}.

$$\frac{3}{4}x^{2}+5x$$

Expand

$$\frac{3x^{2}}{4}+5x$$

Solution Steps

Use the distributive property to multiply \frac{1}{2}x-y by y-\frac{1}{2}x and combine like terms.

$$-6xy+xy-\frac{1}{4}x^{2}-y^{2}+5x\left(y+1\right)-\left(-x^{2}-y^{2}\right)$$

Combine -6xy and xy to get -5xy.

$$-5xy-\frac{1}{4}x^{2}-y^{2}+5x\left(y+1\right)-\left(-x^{2}-y^{2}\right)$$

Use the distributive property to multiply 5x by y+1.

$$-5xy-\frac{1}{4}x^{2}-y^{2}+5xy+5x-\left(-x^{2}-y^{2}\right)$$

Combine -5xy and 5xy to get 0.

$$-\frac{1}{4}x^{2}-y^{2}+5x-\left(-x^{2}-y^{2}\right)$$

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

$$-\frac{1}{4}x^{2}-y^{2}+5x-\left(-x^{2}\right)+y^{2}$$

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

$$-\frac{1}{4}x^{2}+5x-\left(-x^{2}\right)$$

Multiply -1 and -1 to get 1.

$$-\frac{1}{4}x^{2}+5x+x^{2}$$

Combine -\frac{1}{4}x^{2} and x^{2} to get \frac{3}{4}x^{2}.

$$\frac{3}{4}x^{2}+5x$$