Solve 3(x+y)-(x+y)^2=

$$3 ( x + y ) - ( x + y ) ^ { 2 } =$$

Evaluate

$$\left(3-y-x\right)\left(x+y\right)$$

Solution Steps

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

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

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

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

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

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

Expand

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

Solution Steps

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

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

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

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

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

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