Question 147680
{{{(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))=(8*4)*sqrt(6*6)=32*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))=(8*-5)*sqrt(6*2)=-40*2*sqrt(3)=-80*sqrt(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))=(3*4)*sqrt(2*6)=12*2*sqrt(3)=24*sqrt(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))=(3*-5)*sqrt(2*2)=-15*2=-30}}}.



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



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



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



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