Question

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

Answer 1

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`