Solve (x-1)^2-10(x-1)+25

$$( x - 1 ) ^ { 2 } - 10 ( x - 1 ) + 25$$

Evaluate

$$\left(x-6\right)^{2}$$

Solution Steps

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

$$x^{2}-2x+1-10\left(x-1\right)+25$$

Use the distributive property to multiply -10 by x-1.

$$x^{2}-2x+1-10x+10+25$$

Combine -2x and -10x to get -12x.

$$x^{2}-12x+1+10+25$$

Add 1 and 10 to get 11.

$$x^{2}-12x+11+25$$

Add 11 and 25 to get 36.

$$x^{2}-12x+36$$

Expand

$$x^{2}-12x+36$$

Solution Steps

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

$$x^{2}-2x+1-10\left(x-1\right)+25$$

Use the distributive property to multiply -10 by x-1.

$$x^{2}-2x+1-10x+10+25$$

Combine -2x and -10x to get -12x.

$$x^{2}-12x+1+10+25$$

Add 1 and 10 to get 11.

$$x^{2}-12x+11+25$$

Add 11 and 25 to get 36.

$$x^{2}-12x+36$$