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

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

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}.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

The square of \sqrt{3} is 3.

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

Multiply 4 and 3 to get 12.

$$12-\left(\sqrt{7}\right)^{2}$$

The square of \sqrt{7} is 7.

$$12-7$$

Subtract 7 from 12 to get 5.

$$5$$

Factor

$$5$$