Question 582737
{{{(1-sqrt(5))(1+sqrt(5))}}} Start with the given expression.



Now let's FOIL the expression.



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



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



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



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



{{{(1+highlight(-sqrt(5)))(1+highlight(sqrt(5)))}}} Multiply the <font color="red">L</font>ast terms:{{{(-sqrt(5))*(sqrt(5))=-(sqrt(5))^2}}}.



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So we have the terms: {{{1}}}, {{{sqrt(5)}}}, {{{-sqrt(5)}}}, {{{-(sqrt(5))^2}}} 



{{{1+sqrt(5)-sqrt(5)-(sqrt(5))^2}}} Now add every term listed above to make a single expression.



{{{1-(sqrt(5))^2}}} Now combine like terms.



{{{1-5}}} Square {{{sqrt(5)}}} to get 5.



{{{-4}}} Subtract



So {{{(1-sqrt(5))(1+sqrt(5))}}} FOILs and simplifies to {{{-4}}}.



In other words, {{{(1-sqrt(5))(1+sqrt(5))=-4}}}.