Question

How do you expand and simplify each expression `(-sqrt6 + 2)(2sqrt2 - 3sqrt5 + 1)`?

Answer 1

Start by using the distributive property then see if any roots can be simplified.

`(color(red)(-sqrt(6))+color(green)(2))(2sqrt(2) - 3sqrt(5) + 1)`

#= color(red)((-sqrt(6))(2sqrt(2) - 3sqrt(5) + 1)) color(green)(+(2)(2sqrt(2) - 3sqrt(5) +1)#

#= color(red)(-2sqrt(12) +3sqrt(30) -sqrt(6)) color(green)(+ 4sqrt(2) -6sqrt(5) + 2)#

`= -4sqrt(3) + 3sqrt(30) - sqrt(6) +4sqrt(2) -6sqrt(5) + 2`