Question 183026


{{{(5sqrt(2)+2sqrt(3))(sqrt(2)-2sqrt(3))}}} Start with the given expression.



Now let's FOIL the expression.



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



{{{(highlight(5sqrt(2))+2sqrt(3))(highlight(sqrt(2))-2sqrt(3))}}} Multiply the <font color="red">F</font>irst terms:{{{(5*sqrt(2))*(sqrt(2))=10}}}.



{{{(highlight(5sqrt(2))+2sqrt(3))(sqrt(2)+highlight(-2sqrt(3)))}}} Multiply the <font color="red">O</font>uter terms:{{{(5*sqrt(2))*(-2*sqrt(3))=-10*sqrt(6)}}}.



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



{{{(5sqrt(2)+highlight(2sqrt(3)))(sqrt(2)+highlight(-2sqrt(3)))}}} Multiply the <font color="red">L</font>ast terms:{{{(2*sqrt(3))*(-2*sqrt(3))=-12}}}.



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So we have the terms: {{{10}}}, {{{-10*sqrt(6)}}}, {{{2*sqrt(6)}}}, and {{{-12}}} 



{{{10-10*sqrt(6)+2*sqrt(6)-12}}} Now collect every term listed above to make a single expression.



{{{-2-8*sqrt(6)}}} Now combine like terms.



So {{{(5sqrt(2)+2sqrt(3))(sqrt(2)-2sqrt(3))}}} FOILs to {{{-2-8*sqrt(6)}}}.



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