Question 190640


{{{(3sqrt(10)+1)(3sqrt(5)+4)}}} Start with the given expression.



Now let's FOIL the expression.



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



{{{(highlight(3sqrt(10))+1)(highlight(3sqrt(5))+4)}}} Multiply the <font color="red">F</font>irst terms:{{{(3*sqrt(10))*(3*sqrt(5))=45*sqrt(2)}}}.



{{{(highlight(3sqrt(10))+1)(3sqrt(5)+highlight(4))}}} Multiply the <font color="red">O</font>uter terms:{{{(3*sqrt(10))*(4)=12*sqrt(10)}}}.



{{{(3sqrt(10)+highlight(1))(highlight(3sqrt(5))+4)}}} Multiply the <font color="red">I</font>nner terms:{{{(1)*(3*sqrt(5))=3*sqrt(5)}}}.



{{{(3sqrt(10)+highlight(1))(3sqrt(5)+highlight(4))}}} Multiply the <font color="red">L</font>ast terms:{{{(1)*(4)=4}}}.



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So we have the terms: {{{45*sqrt(2)}}}, {{{12*sqrt(10)}}}, {{{3*sqrt(5)}}}, {{{4}}} 



{{{45*sqrt(2)+12*sqrt(10)+3*sqrt(5)+4}}} Now add every term listed above to make a single expression.



So {{{(3sqrt(10)+1)(3sqrt(5)+4)}}} FOILs to {{{45*sqrt(2)+12*sqrt(10)+3*sqrt(5)+4}}}.



In other words, {{{(3sqrt(10)+1)(3sqrt(5)+4)=45*sqrt(2)+12*sqrt(10)+3*sqrt(5)+4}}}.