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

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

Evaluate

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

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

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

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

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

Combine x^{2} and x^{2} to get 2x^{2}.

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

Expand

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

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

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

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

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

Combine x^{2} and x^{2} to get 2x^{2}.

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