Question 169973


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



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



{{{(highlight(sqrt(2))-5)(sqrt(2)+highlight(-5))}}} Multiply the <font color="red">O</font>uter terms:{{{(sqrt(2))*(-5)=-5*sqrt(2)}}}.



{{{(sqrt(2)+highlight(-5))(highlight(sqrt(2))-5)}}} Multiply the <font color="red">I</font>nner terms:{{{(-5)*(sqrt(2))=-5*sqrt(2)}}}.



{{{(sqrt(2)+highlight(-5))(sqrt(2)+highlight(-5))}}} Multiply the <font color="red">L</font>ast terms:{{{(-5)*(-5)=25}}}.



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{{{2-5*sqrt(2)-5*sqrt(2)+25}}} Now collect every term to make a single expression.



{{{27-10*sqrt(2)}}} Now combine like terms.



So {{{(sqrt(2)-5)^2}}} FOILs to {{{27-10*sqrt(2)}}}.



In other words, {{{(sqrt(2)-5)^2=27-10*sqrt(2)}}}.