How do you multiply #(6-[3sqrt2])(6+[3sqrt2])#?

1 Answer
Jul 24, 2015

Answer:

#(6-[3sqrt(2])(6+[3sqrt(2)])#
#color(white)("XXXX")##color(white)("XXXX")##color(white)("XXXX")##color(white)("XXXX")##= 18#

Explanation:

In general
#color(white)("XXXX")##(a+b)(a-b) = a^2-b^2#
(this is commonly referred to as the difference of quares)

So
#color(white)("XXXX")##(6-[3sqrt(2])(6+[3sqrt(2)])#

#color(white)("XXXX")##color(white)("XXXX")##= 6^2 - [3sqrt(2)]^2#

#color(white)("XXXX")##color(white)("XXXX")##= 36 - 18#

#color(white)("XXXX")##color(white)("XXXX")##= 18#