Question 195531


{{{(sqrt(5)-sqrt(7))^2}}} Start with the given expression.



{{{(sqrt(5)-sqrt(7))(sqrt(5)-sqrt(7))}}} Expand. Remember something like {{{x^2=x*x}}}.



Now let's FOIL the expression.



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



{{{(highlight(sqrt(5))-sqrt(7))(highlight(sqrt(5))-sqrt(7))}}} Multiply the <font color="red">F</font>irst terms:{{{(sqrt(5))*(sqrt(5))=sqrt(5*5)=sqrt(25)=5}}}.



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



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



{{{(sqrt(5)+highlight(-sqrt(7)))(sqrt(5)+highlight(-sqrt(7)))}}} Multiply the <font color="red">L</font>ast terms:{{{(-sqrt(7))*(-sqrt(7))=sqrt(7*7)=sqrt(49)=7}}}.



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So we have the terms: {{{5}}}, {{{-sqrt(35)}}}, {{{-sqrt(35)}}}, and {{{7}}} 



{{{5-sqrt(35)-sqrt(35)+7}}} Now add every term listed above to make a single expression.



{{{12-2*sqrt(35)}}} Now combine like terms.



So {{{(sqrt(5)-sqrt(7))^2}}} FOILs to {{{12-2*sqrt(35)}}}.



In other words, {{{(sqrt(5)-sqrt(7))^2=12-2*sqrt(35)}}}.