Question 195721
{{{(x^5+7x)(x^5-7x)}}} Start with the given expression.



Now let's FOIL the expression.



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



{{{(highlight(x^5)+7x)(highlight(x^5)-7x)}}} Multiply the <font color="red">F</font>irst terms:{{{(x^5)*(x^5)=x^10}}}.



{{{(highlight(x^5)+7x)(x^5+highlight(-7x))}}} Multiply the <font color="red">O</font>uter terms:{{{(x^5)*(-7*x)=-7*x^6}}}.



{{{(x^5+highlight(7x))(highlight(x^5)-7x)}}} Multiply the <font color="red">I</font>nner terms:{{{(7*x)*(x^5)=7*x^6}}}.



{{{(x^5+highlight(7x))(x^5+highlight(-7x))}}} Multiply the <font color="red">L</font>ast terms:{{{(7*x)*(-7*x)=-49*x^2}}}.



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So we have the terms: {{{x^10}}}, {{{-7*x^6}}}, {{{7*x^6}}}, and {{{-49*x^2}}} 



{{{x^10-7*x^6+7*x^6-49*x^2}}} Now add every term listed above to make a single expression.



{{{x^10-49*x^2}}} Now combine like terms.



So {{{(x^5+7x)(x^5-7x)}}} FOILs to {{{x^10-49*x^2}}}.



In other words, {{{(x^5+7x)(x^5-7x)=x^10-49*x^2}}}.