Question 243234


{{{(2-5x^8)^2}}} Start with the given expression.



{{{(2-5x^8)(2-5x^8)}}} Expand. Remember something like {{{x^2=x*x}}}.



Now let's FOIL the expression.



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



{{{(highlight(2)-5x^8)(highlight(2)-5x^8)}}} Multiply the <font color="red">F</font>irst terms:{{{(2)*(2)=4}}}.



{{{(highlight(2)-5x^8)(2+highlight(-5x^8))}}} Multiply the <font color="red">O</font>uter terms:{{{(2)*(-5*x^8)=-10*x^8}}}.



{{{(2+highlight(-5x^8))(highlight(2)-5x^8)}}} Multiply the <font color="red">I</font>nner terms:{{{(-5*x^8)*(2)=-10*x^8}}}.



{{{(2+highlight(-5x^8))(2+highlight(-5x^8))}}} Multiply the <font color="red">L</font>ast terms:{{{(-5*x^8)*(-5*x^8)=25*x^16}}}.



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So we have the terms: {{{4}}}, {{{-10*x^8}}}, {{{-10*x^8}}}, and {{{25*x^16}}} 



{{{4-10*x^8-10*x^8+25*x^16}}} Now add every term listed above to make a single expression.



{{{4-20*x^8+25*x^16}}} Now combine like terms.



So {{{(2-5x^8)^2}}} FOILs to {{{4-20*x^8+25*x^16}}}.



In other words, {{{(2-5x^8)^2=4-20*x^8+25*x^16}}}.