Solve (2sqrt{3}-4)(2sqrt{3}+4)-(3-2

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

Evaluate

$$-5$$

Solution Steps

Consider \left(2\sqrt{3}-4\right)\left(2\sqrt{3}+4\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Expand \left(2\sqrt{3}\right)^{2}.

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

Calculate 2 to the power of 2 and get 4.

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

The square of \sqrt{3} is 3.

$$4\times 3-4^{2}-\left(3-2\right)$$

Multiply 4 and 3 to get 12.

$$12-4^{2}-\left(3-2\right)$$

Calculate 4 to the power of 2 and get 16.

$$12-16-\left(3-2\right)$$

Subtract 16 from 12 to get -4.

$$-4-\left(3-2\right)$$

Subtract 2 from 3 to get 1.

$$-4-1$$

Subtract 1 from -4 to get -5.

$$-5$$

Factor

$$-5$$