Solve (5sqrt{3}-6)*(-14sqrt{3}-5)-(-10sqrt{3}-3)*(7sqrt{3}-10)

$$(5 \sqrt{ 3 } -6) \times (-14 \sqrt{ 3 } -5)-(-10 \sqrt{ 3 } -3) \times (7 \sqrt{ 3 } -10)$$

Evaluate

$$-20\sqrt{3}\approx -34.641016151$$

Solution Steps

Apply the distributive property by multiplying each term of 5\sqrt{3}-6 by each term of -14\sqrt{3}-5.

$$-70\left(\sqrt{3}\right)^{2}-25\sqrt{3}+84\sqrt{3}+30-\left(-10\sqrt{3}-3\right)\left(7\sqrt{3}-10\right)$$

The square of \sqrt{3} is 3.

$$-70\times 3-25\sqrt{3}+84\sqrt{3}+30-\left(-10\sqrt{3}-3\right)\left(7\sqrt{3}-10\right)$$

Multiply -70 and 3 to get -210.

$$-210-25\sqrt{3}+84\sqrt{3}+30-\left(-10\sqrt{3}-3\right)\left(7\sqrt{3}-10\right)$$

Combine -25\sqrt{3} and 84\sqrt{3} to get 59\sqrt{3}.

$$-210+59\sqrt{3}+30-\left(-10\sqrt{3}-3\right)\left(7\sqrt{3}-10\right)$$

Add -210 and 30 to get -180.

$$-180+59\sqrt{3}-\left(-10\sqrt{3}-3\right)\left(7\sqrt{3}-10\right)$$

Apply the distributive property by multiplying each term of -10\sqrt{3}-3 by each term of 7\sqrt{3}-10.

$$-180+59\sqrt{3}-\left(-70\left(\sqrt{3}\right)^{2}+100\sqrt{3}-21\sqrt{3}+30\right)$$

The square of \sqrt{3} is 3.

$$-180+59\sqrt{3}-\left(-70\times 3+100\sqrt{3}-21\sqrt{3}+30\right)$$

Multiply -70 and 3 to get -210.

$$-180+59\sqrt{3}-\left(-210+100\sqrt{3}-21\sqrt{3}+30\right)$$

Combine 100\sqrt{3} and -21\sqrt{3} to get 79\sqrt{3}.

$$-180+59\sqrt{3}-\left(-210+79\sqrt{3}+30\right)$$

Add -210 and 30 to get -180.

$$-180+59\sqrt{3}-\left(-180+79\sqrt{3}\right)$$

To find the opposite of -180+79\sqrt{3}, find the opposite of each term.

$$-180+59\sqrt{3}-\left(-180\right)-79\sqrt{3}$$

The opposite of -180 is 180.

$$-180+59\sqrt{3}+180-79\sqrt{3}$$

Add -180 and 180 to get 0.

$$59\sqrt{3}-79\sqrt{3}$$

Combine 59\sqrt{3} and -79\sqrt{3} to get -20\sqrt{3}.

$$-20\sqrt{3}$$