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

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

Evaluate

$$x^{2}$$

Solution Steps

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

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

Subtract 2 from 1 to get -1.

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

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

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

Add -1 and 1 to get 0.

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

Combine 2x and -2x to get 0.

$$x^{2}$$

Expand

$$x^{2}$$

Solution Steps

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

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

Subtract 2 from 1 to get -1.

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

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

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

Add -1 and 1 to get 0.

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

Combine 2x and -2x to get 0.

$$x^{2}$$