Question 131914

{{{(3*sqrt(3)-6*sqrt(6))(5*sqrt(3)+10*sqrt(6))}}} Start with the given expression



Now let's FOIL the expression




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



{{{(highlight(3*sqrt(3))-6*sqrt(6))(highlight(5*sqrt(3))+10*sqrt(6))}}} Multiply the First terms:{{{(3*sqrt(3))*(5*sqrt(3))=3*5*sqrt(3*3)=15*sqrt(9)=15*3=45}}}



{{{(highlight(3*sqrt(3))-6*sqrt(6))(5*sqrt(3)+highlight(10*sqrt(6)))}}} Multiply the Outer terms:{{{(3*sqrt(3))*(10*sqrt(6))=3*10*sqrt(3*6)=30*3*sqrt(2)=90*sqrt(2)}}}



{{{(3*sqrt(3)+highlight(-6*sqrt(6)))(highlight(5*sqrt(3))+10*sqrt(6))}}} Multiply the Inner terms:{{{(-6*sqrt(6))*(5*sqrt(3))=-30*3*sqrt(2)=-90*sqrt(2)}}}



{{{(3*sqrt(3)+highlight(-6*sqrt(6)))(5*sqrt(3)+highlight(10*sqrt(6)))}}} Multiply the Last terms:{{{(-6*sqrt(6))*(10*sqrt(6))=-6*10*sqrt(6*6)=-60*6=-360}}}



{{{45+90*sqrt(2)-90*sqrt(2)-360}}} Now collect every term to make a single expression



{{{-315}}} Combine like terms



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Answer:

So {{{(3*sqrt(3)-6*sqrt(6))(5*sqrt(3)+10*sqrt(6))}}} foils and simplifies to  {{{-315}}}


In other words, {{{(3*sqrt(3)-6*sqrt(6))(5*sqrt(3)+10*sqrt(6))=-315}}}