Solve (sqrt{7}-2sqrt{3})(sqrt{7}+2sqrt{3})

$$( \sqrt { 7 } - 2 \sqrt { 3 } ) ( \sqrt { 7 } + 2 \sqrt { 3 } )$$

Evaluate

$$-5$$

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}.

$$\left(\sqrt{7}\right)^{2}-\left(2\sqrt{3}\right)^{2}$$

The square of \sqrt{7} is 7.

$$7-\left(2\sqrt{3}\right)^{2}$$

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

$$7-2^{2}\left(\sqrt{3}\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

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

The square of \sqrt{3} is 3.

$$7-4\times 3$$

Multiply 4 and 3 to get 12.

$$7-12$$

Subtract 12 from 7 to get -5.

$$-5$$

Factor

$$-5$$