Question 190606


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



Now let's FOIL the expression.



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



{{{(highlight(2)+sqrt(7))(highlight(2)-sqrt(7))}}} Multiply the <font color="red">F</font>irst terms:{{{(2)*(2)=4}}}.



{{{(highlight(2)+sqrt(7))(2+highlight(-sqrt(7)))}}} Multiply the <font color="red">O</font>uter terms:{{{(2)*(-sqrt(7))=-2*sqrt(7)}}}.



{{{(2+highlight(sqrt(7)))(highlight(2)-sqrt(7))}}} Multiply the <font color="red">I</font>nner terms:{{{(sqrt(7))*(2)=2*sqrt(7)}}}.



{{{(2+highlight(sqrt(7)))(2+highlight(-sqrt(7)))}}} Multiply the <font color="red">L</font>ast terms:{{{(sqrt(7))*(-sqrt(7))=-sqrt(49)=-7}}}.



---------------------------------------------------

So we have the terms: {{{4}}}, {{{-2*sqrt(7)}}}, {{{2*sqrt(7)}}}, and {{{-7}}} 



{{{4-2*sqrt(7)+2*sqrt(7)-7}}} Now add every term listed above to make a single expression.



{{{-3}}} Now combine like terms.



So {{{(2+sqrt(7))(2-sqrt(7))}}} FOILs to {{{-3}}}.



In other words, {{{(2+sqrt(7))(2-sqrt(7))=-3}}}.