Question 211308

{{{(5*sqrt(7)-15*sqrt(5))(4*sqrt(7)-12*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(7))-15*sqrt(5))(highlight(4*sqrt(7))-12*sqrt(5))}}} Multiply the <font color="red">F</font>irst terms:{{{(5*sqrt(7))*(4*sqrt(7))=5*4*sqrt(7*7)=20*sqrt(49)=20*7=140}}}.



{{{(highlight(5*sqrt(7))-15*sqrt(5))(4*sqrt(7)+highlight(-12*sqrt(5)))}}} Multiply the <font color="red">O</font>uter terms:{{{(5*sqrt(7))*(-12*sqrt(5))=-5*12*sqrt(7*5)=-60*sqrt(35)}}}.



{{{(5*sqrt(7)+highlight(-15*sqrt(5)))(highlight(4*sqrt(7))-12*sqrt(5))}}} Multiply the <font color="red">I</font>nner terms:{{{(-15*sqrt(5))*(4*sqrt(7))=-15*4*sqrt(5*7)=-60*sqrt(35)}}}.



{{{(5*sqrt(7)+highlight(-15*sqrt(5)))(4*sqrt(7)+highlight(-12*sqrt(5)))}}} Multiply the <font color="red">L</font>ast terms:{{{(-15*sqrt(5))*(-12*sqrt(5))=-15*(-12)*sqrt(5*5)=180*sqrt(25)=180*5=900}}}.



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So we have the terms: {{{140}}}, {{{-60*sqrt(35)}}}, {{{-60*sqrt(35)}}}, and {{{900}}} 



{{{140-60*sqrt(35)-60*sqrt(35)+900}}} Now add every term listed above to make a single expression.



{{{1040-120*sqrt(35)}}} Combine like terms.



So {{{(5*sqrt(7)-15*sqrt(5))(4*sqrt(7)-12*sqrt(5))}}} FOILs to {{{1040-120*sqrt(35)}}}.



In other words, {{{(5*sqrt(7)-15*sqrt(5))(4*sqrt(7)-12*sqrt(5))=1040-120*sqrt(35)}}}.