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

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

Evaluate

$$\left(x-y\right)\left(x-y+1\right)$$

Solution Steps

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

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

To find the opposite of y-x, find the opposite of each term.

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

Expand

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

Solution Steps

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

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

To find the opposite of y-x, find the opposite of each term.

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