Solve (5-2sqrt{3})(5+2sqrt{3})

$$(5-2 \sqrt{ 3 } )(5+2 \sqrt{ 3 } )$$

Evaluate

$$13$$

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}.

$$5^{2}-\left(2\sqrt{3}\right)^{2}$$

Calculate 5 to the power of 2 and get 25.

$$25-\left(2\sqrt{3}\right)^{2}$$

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

$$25-2^{2}\left(\sqrt{3}\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$25-4\left(\sqrt{3}\right)^{2}$$

The square of \sqrt{3} is 3.

$$25-4\times 3$$

Multiply 4 and 3 to get 12.

$$25-12$$

Subtract 12 from 25 to get 13.

$$13$$

Factor

$$13$$