Question 257280
{{{(sqrt(8)+3*sqrt(10))(sqrt(8)-3*sqrt(10))}}} Start with the given expression.



Let {{{x=sqrt(8)}}} and {{{y=3*sqrt(10)}}}


{{{(x+y)(x-y)}}} Replace each {{{sqrt(8)}}} term with "x" and each {{{3*sqrt(10)}}} term with "y"



Now let's FOIL the expression.



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



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



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



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



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



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So we have the terms: {{{x^2}}}, {{{-x*y}}}, {{{x*y}}}, {{{-y^2}}} 



{{{x^2-x*y+x*y-y^2}}} Now add every term listed above to make a single expression.



{{{x^2-y^2}}} Now combine like terms.



So {{{(x+y)(x-y)}}} FOILs to {{{x^2-y^2}}}.



In other words, {{{(x+y)(x-y)=x^2-y^2}}}.



{{{(sqrt(8)+3*sqrt(10))(sqrt(8)-3*sqrt(10))=(sqrt(8))^2-(3*sqrt(10))^2}}} Now plug in {{{x=sqrt(8)}}} and {{{y=3*sqrt(10)}}}



{{{8-(3*sqrt(10))^2}}} Square {{{sqrt(8)}}} to get 8.



{{{8-90}}} Square {{{3*sqrt(10)}}} to get {{{(3*sqrt(10))^2=9*10=90}}}.



{{{-82}}} Subtract.



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Answer:



So {{{(sqrt(8)+3*sqrt(10))(sqrt(8)-3*sqrt(10))=-82}}}