How do you simplify (6+ sqrt3)(6-sqrt3)?

May 28, 2015

You may find it helpful to use the mnemonic FOIL - First, Outside, Inside, Last.

That means multiply both first terms together ($6 \times 6$),
add the product of the outside terms ($6 \times - \sqrt{3}$)
add the product of the inside terms ($\sqrt{3} \times 6$)
add the product of the last terms ($\sqrt{3} \times - \sqrt{3}$)

So

$\left(6 + \sqrt{3}\right) \left(6 - \sqrt{3}\right)$

$= {6}^{2} - \cancel{6 \sqrt{3}} + \cancel{6 \sqrt{3}} - {\sqrt{3}}^{2}$

$= 36 - 3 = 33$

Alternatively, you could use the identity of difference of squares:

${a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$

to get:

$\left(6 + \sqrt{3}\right) \left(6 - \sqrt{3}\right) = {6}^{2} - {\sqrt{3}}^{2} = 36 - 3 = 33$