Solve (x-y)^2-5(x-y)=

$$( x - y ) ^ { 2 } - 5 ( x - y ) =$$

Evaluate

$$\left(x-y\right)\left(x-y-5\right)$$

Solution Steps

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

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

Use the distributive property to multiply -5 by x-y.

$$x^{2}-2xy+y^{2}-5x+5y$$

Expand

$$x^{2}-2xy-5x+y^{2}+5y$$

Solution Steps

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

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

Use the distributive property to multiply -5 by x-y.

$$x^{2}-2xy+y^{2}-5x+5y$$