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

May 25, 2015

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.

'First' : $\left(4 \sqrt{3} \cdot 2 \sqrt{3}\right) = 24$
'Outside': $\left(4 \sqrt{3} \cdot 3 \sqrt{2}\right) = 12 \sqrt{6}$
'Inside': $\left(- 5 \sqrt{2} \cdot 2 \sqrt{3}\right) = - 10 \sqrt{6}$
'Last': $\left(- 5 \sqrt{2} \cdot 3 \sqrt{2}\right) = - 30$

$\left(4 \sqrt{3} - 5 \sqrt{2}\right) \left(2 \sqrt{3} + 3 \sqrt{2}\right)$
($= F + O + I + L$ )
$= 24 + 12 \sqrt{6} - 10 \sqrt{6} - 30$
$= 2 \sqrt{6} - 6$