Solve 2sqrt{3}-11^2-(sqrt{3}+2)^2

$$2 \sqrt { 3 } - 11 ^ { 2 } - ( \sqrt { 3 } + 2 ) ^ { 2 }$$

Evaluate

$$-2\sqrt{3}-128\approx -131.464101615$$

Solution Steps

Calculate 11 to the power of 2 and get 121.

$$2\sqrt{3}-121-\left(\sqrt{3}+2\right)^{2}$$

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

$$2\sqrt{3}-121-\left(\left(\sqrt{3}\right)^{2}+4\sqrt{3}+4\right)$$

The square of \sqrt{3} is 3.

$$2\sqrt{3}-121-\left(3+4\sqrt{3}+4\right)$$

Add 3 and 4 to get 7.

$$2\sqrt{3}-121-\left(7+4\sqrt{3}\right)$$

To find the opposite of 7+4\sqrt{3}, find the opposite of each term.

$$2\sqrt{3}-121-7-4\sqrt{3}$$

Subtract 7 from -121 to get -128.

$$2\sqrt{3}-128-4\sqrt{3}$$

Combine 2\sqrt{3} and -4\sqrt{3} to get -2\sqrt{3}.

$$-2\sqrt{3}-128$$