Question 176963
First, let's multiply out {{{(x+1)(x-1)}}}



{{{(x+1)(x-1)}}} Start with the given expression.



Now let's FOIL the expression.



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



{{{(highlight(x)+1)(highlight(x)-1)}}} Multiply the <font color="red">F</font>irst terms:{{{(x)*(x)=x^2}}}.



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



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



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



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{{{x^2-x+x-1}}} Now collect every term to make a single expression.



{{{x^2-1}}} Now combine like terms.



So {{{(x+1)(x-1)}}} FOILs to {{{x^2-1}}}.



In other words, {{{(x+1)(x-1)=x^2-1}}}.



So this means that {{{x(x+1)(x-1)=x(x^2-1)}}}



{{{x(x^2-1)}}} Start with the given expression.



{{{x^3-x}}} Distribute



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Answer:


So {{{x(x+1)(x-1)=x^3-x}}}