Solve left(x-yright)^2+2(x-y)+1

$${ \left(x-y \right) }^{ 2 } +2(x-y)+1$$

Evaluate

$$\left(x-y+1\right)^{2}$$

Solution Steps

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

$$x^{2}-2xy+y^{2}+2\left(x-y\right)+1$$

Use the distributive property to multiply 2 by x-y.

$$x^{2}-2xy+y^{2}+2x-2y+1$$

Expand

$$x^{2}-2xy+2x+y^{2}-2y+1$$

Solution Steps

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

$$x^{2}-2xy+y^{2}+2\left(x-y\right)+1$$

Use the distributive property to multiply 2 by x-y.

$$x^{2}-2xy+y^{2}+2x-2y+1$$