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

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

Evaluate

$$11$$

Solution Steps

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

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

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

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

Calculate 2 to the power of 2 and get 4.

$$4\left(\sqrt{3}\right)^{2}-1^{2}$$

The square of \sqrt{3} is 3.

$$4\times 3-1^{2}$$

Multiply 4 and 3 to get 12.

$$12-1^{2}$$

Calculate 1 to the power of 2 and get 1.

$$12-1$$

Subtract 1 from 12 to get 11.

$$11$$

Factor

$$11$$