How do you simplify #(4sqrt3 - 5sqrt2 ) * (2sqrt3 + 3sqrt2)#?

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Answer 1 · 2015-04-02T17:35:33

#(4sqrt(3) - 5sqrt(2)) * (2sqrt(3) + 3sqrt(2)) = #

#4sqrt(3) * 2sqrt(3) + 4sqrt(3) * 3sqrt(2) -5sqrt(2) * 2sqrt(3) -5sqrt(2) * 3sqrt(2) = #

#8sqrt(3*3) +12sqrt(3*2) -10sqrt(2*3) -15sqrt(2*2) = #

#8sqrt(3^2) + 12sqrt(6) - 10sqrt(6) - 15sqrt(2^2) = #

#8*3 + 12sqrt(6) - 10sqrt(6) - 15*2 = #

#24 + sqrt(6) * (12 - 10) - 30 = #

Answer: #2sqrt(6) - 6#