Question

How do you FOIL `(4√ 3 - 5√ 2 ) * (2√ 3 + 3√ 2)`?

Answer 1

FOIL is short for First, Outside, Inside, Last
It helps you to remember all the combinations when multiplying two bracketed terms each containing two expressions.

For your example, we have

'First' : `(4sqrt(3)*2sqrt(3)) = 24`
'Outside': `(4sqrt(3)*3sqrt(2)) = 12sqrt(6)`
'Inside': `(-5sqrt(2)*2sqrt(3)) = -10sqrt(6)`
'Last': `(-5sqrt(2)*3sqrt(2)) = -30`

Add these together to get the answer:

`(4sqrt(3)-5sqrt(2))(2sqrt(3)+3sqrt(2))`

(`= F + O + I + L` )

`= 24+12sqrt(6)-10sqrt(6)-30`

`= 2sqrt(6)-6`