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

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

Evaluate

$$10$$

Solution Steps

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

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

The square of \sqrt{3} is 3.

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

Add 1 and 3 to get 4.

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

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

$$4-2\sqrt{3}+6+2\sqrt{3}$$

Add 4 and 6 to get 10.

$$10-2\sqrt{3}+2\sqrt{3}$$

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

$$10$$

Factor

$$2\times 5$$