Question 190604


{{{(sqrt(2)+3)(sqrt(3)-4)}}} Start with the given expression.



Now let's FOIL the expression.



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



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



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



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



{{{(sqrt(2)+highlight(3))(sqrt(3)+highlight(-4))}}} Multiply the <font color="red">L</font>ast terms:{{{(3)*(-4)=-12}}}.



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So we have the terms: {{{sqrt(6)}}}, {{{-4*sqrt(2)}}}, {{{3*sqrt(3)}}}, {{{-12}}} 



{{{sqrt(6)-4*sqrt(2)+3*sqrt(3)-12}}} Now add every term listed above to make a single expression.



So {{{(sqrt(2)+3)(sqrt(3)-4)}}} FOILs to {{{sqrt(6)-4*sqrt(2)+3*sqrt(3)-12}}}.



In other words, {{{(sqrt(2)+3)(sqrt(3)-4)=sqrt(6)-4*sqrt(2)+3*sqrt(3)-12}}}.