Solve (1-sqrt{3})^2-2(1-sqrt{3})

$$( 1 - \sqrt { 3 } ) ^ { 2 } - 2 ( 1 - \sqrt { 3 } )$$

Evaluate

$$2$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(1-\sqrt{3}\right)^{2}.

$$1-2\sqrt{3}+\left(\sqrt{3}\right)^{2}-2\left(1-\sqrt{3}\right)$$

The square of \sqrt{3} is 3.

$$1-2\sqrt{3}+3-2\left(1-\sqrt{3}\right)$$

Add 1 and 3 to get 4.

$$4-2\sqrt{3}-2\left(1-\sqrt{3}\right)$$

Use the distributive property to multiply -2 by 1-\sqrt{3}.

$$4-2\sqrt{3}-2+2\sqrt{3}$$

Subtract 2 from 4 to get 2.

$$2-2\sqrt{3}+2\sqrt{3}$$

Combine -2\sqrt{3} and 2\sqrt{3} to get 0.

$$2$$

Factor

$$2$$