How do you simplify #(8sqrt[6] + 3sqrt[2])(4sqrt[6] – 5sqrt[2])#?

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Answer 1 · 2017-12-01T19:31:22

Use binomial multiplication (FOIL)

Going directly to the solution and not rewriting the problem, binomial multiplication gives:

#8sqrt6*4sqrt6-8sqrt6*5sqrt2+3sqrt2*4sqrt6-3sqrt2*5sqrt2#

Simplifying:
#32sqrt6^2-40sqrt12+12sqrt12-15sqrt2^2#

Next:
#32*6-28sqrt12-15*2#

#192-28sqrt12-30#

#162-28sqrt12#

Then simplify #sqrt12=sqrt{4*3}=2sqrt3#

So, #162-28*2sqrt3 = 162-56sqrt3#