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

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

Evaluate

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

Solution Steps

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

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

Use the distributive property to multiply -2a by x-1.

$$x^{2}-2x+1+a^{2}-2ax+2a$$

Expand

$$x^{2}-2ax-2x+a^{2}+2a+1$$

Solution Steps

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

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

Use the distributive property to multiply -2a by x-1.

$$x^{2}-2x+1+a^{2}-2ax+2a$$