How do you multiply (4sqrt3-5sqrt2)(2sqrt3+3sqrt2)(4√3−5√2)(2√3+3√2)?

1 Answer
Truong-Son N.
Jun 11, 2015

You can multiply the first terms, the first and second, then the second and first, then the second terms of each parenthesized group. (FOIL = first, outer, inner, last)

= overbrace([4sqrt3*2sqrt3])^("First") + overbrace([4sqrt3*3sqrt2])^("Outer") + overbrace([-5sqrt2*2sqrt3])^("Inner") + overbrace([-5sqrt2*3sqrt2])^("Last")

= 8*3 + 12sqrt6 - 10sqrt6 - 15*2

= -6 + 2sqrt6

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