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

1 Answer
George C.
May 28, 2015

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

That means multiply both first terms together (#6xx6#),
add the product of the outside terms (#6xx-sqrt(3)#)
add the product of the inside terms (#sqrt(3)xx6#)
add the product of the last terms (#sqrt(3)xx-sqrt(3)#)

So

#(6+sqrt(3))(6-sqrt(3))#

#= 6^2-cancel(6sqrt(3))+cancel(6sqrt(3))-sqrt(3)^2#

#= 36-3 = 33#

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

#a^2-b^2 = (a-b)(a+b)#

to get:

#(6+sqrt(3))(6-sqrt(3)) = 6^2-sqrt(3)^2 = 36 - 3 = 33#

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