Question 167727

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



Now let's FOIL the expression.



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



{{{(highlight(5*sqrt(3))+sqrt(5))(highlight(sqrt(3))-2*sqrt(5))}}} Multiply the <font color="red">F</font>irst terms:{{{(5*sqrt(3))*(sqrt(3))=5*sqrt(3*3)=5*3=15}}}.



{{{(highlight(5*sqrt(3))+sqrt(5))(sqrt(3)+highlight(-2*sqrt(5)))}}} Multiply the <font color="red">O</font>uter terms:{{{(5*sqrt(3))*(-2*sqrt(5))=5(-2)*sqrt(3*5)=-10*sqrt(15)}}}.



{{{(5*sqrt(3)+highlight(sqrt(5)))(highlight(sqrt(3))-2*sqrt(5))}}} Multiply the <font color="red">I</font>nner terms:{{{(sqrt(5))*(sqrt(3))=sqrt(3*5)=sqrt(15)}}}.



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



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{{{15-10*sqrt(15)+sqrt(15)-10}}} Now collect every term to make a single expression.



{{{5-9*sqrt(15)}}} Now combine like terms.



So {{{(5sqrt(3)+sqrt(5))(sqrt(3)-2sqrt(5))}}} FOILs to {{{5-9*sqrt(15)}}}.



In other words, {{{(5*sqrt(3)+sqrt(5))(sqrt(3)-2*sqrt(5))=5-9*sqrt(15)}}}.