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

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

Evaluate

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

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

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

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.

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