Solve (-2sqrt{3}+2)(sqrt{3}-5)

$$( - 2 \sqrt { 3 } + 2 ) ( \sqrt { 3 } - 5 )$$

Evaluate

$$4\left(3\sqrt{3}-4\right)\approx 4.784609691$$

Solution Steps

Apply the distributive property by multiplying each term of -2\sqrt{3}+2 by each term of \sqrt{3}-5.

$$-2\left(\sqrt{3}\right)^{2}+10\sqrt{3}+2\sqrt{3}-10$$

The square of \sqrt{3} is 3.

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

Multiply -2 and 3 to get -6.

$$-6+10\sqrt{3}+2\sqrt{3}-10$$

Combine 10\sqrt{3} and 2\sqrt{3} to get 12\sqrt{3}.

$$-6+12\sqrt{3}-10$$

Subtract 10 from -6 to get -16.

$$-16+12\sqrt{3}$$

Factor

$$4 {(3 \sqrt{3} - 4)} = 4.784609691$$