Solve {l}{(x+y)^2-(x-3)(x+y)}{-2y^2}

$$\left. \begin{array} { l } { ( x + y ) ^ { 2 } - ( x - 3 ) ( x + y ) } \\ { - 2 y ^ { 2 } } \end{array} \right.$$

Evaluate

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

Solution Steps

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

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

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

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

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

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

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

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

Combine 2xy and -xy to get xy.

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

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

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

Expand

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

Solution Steps

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

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

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

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

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

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

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

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

Combine 2xy and -xy to get xy.

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

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

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