Question 146716
{{{(8*sqrt(6) + 3*sqrt(2))(4*sqrt(6) - 5*sqrt(2))}}} Start with the given expression.



Now let's FOIL the expression.



Remember, when you FOIL an expression, you follow this procedure:



{{{(highlight(8*sqrt(6) )+ 3*sqrt(2))(highlight(4*sqrt(6) )- 5*sqrt(2))}}} Multiply the <font color="red">F</font>irst terms:{{{(8*sqrt(6) )*(4*sqrt(6) )=192}}}.



{{{(highlight(8*sqrt(6) )+ 3*sqrt(2))(4*sqrt(6) +highlight(- 5*sqrt(2)))}}} Multiply the <font color="red">O</font>uter terms:{{{(8*sqrt(6) )*(- 5*sqrt(2))=-40sqrt(12)=-80sqrt(3)}}}.



{{{(8*sqrt(6) +highlight( 3*sqrt(2)))(highlight(4*sqrt(6) )- 5*sqrt(2))}}} Multiply the <font color="red">I</font>nner terms:{{{( 3*sqrt(2))*(4*sqrt(6) )=12sqrt(12)=24sqrt(3)}}}.



{{{(8*sqrt(6) +highlight( 3*sqrt(2)))(4*sqrt(6) +highlight(- 5*sqrt(2)))}}} Multiply the <font color="red">L</font>ast terms:{{{( 3*sqrt(2))*(- 5*sqrt(2))=-30}}}.



{{{192-80sqrt(3)+24sqrt(3)-30}}} Now collect every term to make a single expression.



{{{162-56sqrt(3)}}} Now combine like terms.



So {{{(8*sqrt(6) + 3*sqrt(2))(4*sqrt(6) - 5*sqrt(2))}}} FOILS to {{{162-56sqrt(3)}}}.



In other words, {{{(8*sqrt(6) + 3*sqrt(2))(4*sqrt(6) - 5*sqrt(2))=162-56sqrt(3)}}}.