Question 126405
{{{(root(5,4)-root(5,2))(root(5,125)+root(5,8))}}} Start with the given expression



Now let's FOIL the expression




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



{{{(highlight(root(5,4))-root(5,2))(highlight(root(5,125))+root(5,8))}}} Multiply the First terms:{{{(root(5,4))*(root(5,125))=root(5,4*125)=root(5,500)}}}







{{{(highlight(root(5,4))-root(5,2))(root(5,125)+highlight(root(5,8)))}}} Multiply the Outer terms:{{{(root(5,4))*(root(5,8))=root(5,4*8)=root(5,32)}}}



Now simplify {{{root(5,32)}}} to get 2. In other words, {{{root(5,32)=2}}}




{{{(root(5,4)+highlight(-root(5,2)))(highlight(root(5,125))+root(5,8))}}} Multiply the Inner terms:{{{(-root(5,2))*(root(5,125))=-root(5,2*125)=-root(5,250)}}}




{{{(root(5,4)+highlight(-root(5,2)))(root(5,125)+highlight(root(5,8)))}}} Multiply the Last terms:{{{(-root(5,2))*(root(5,8))=-root(5,2*8)=-root(5,16)}}}



{{{root(5,500)+2-root(5,250)-root(5,16)}}} Now collect every term to make a single expression




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Answer:

So {{{(root(5,4)-root(5,2))(root(5,125)+root(5,8))}}} foils and simplifies to  {{{root(5,500)+2-root(5,250)-root(5,16)}}}


In other words, {{{(root(5,4)-root(5,2))(root(5,125)+root(5,8))=root(5,500)+2-root(5,250)-root(5,16)}}}