Question 183219

{{{(3z^4-8)^2}}} Start with the given expression.



{{{(3z^4-8)(3z^4-8)}}} 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(3z^4)-8)(highlight(3z^4)-8)}}} Multiply the <font color="red">F</font>irst terms:{{{(3*z^4)*(3*z^4)=9*z^8}}}.



{{{(highlight(3z^4)-8)(3z^4+highlight(-8))}}} Multiply the <font color="red">O</font>uter terms:{{{(3*z^4)*(-8)=-24*z^4}}}.



{{{(3z^4+highlight(-8))(highlight(3z^4)-8)}}} Multiply the <font color="red">I</font>nner terms:{{{(-8)*(3*z^4)=-24*z^4}}}.



{{{(3z^4+highlight(-8))(3z^4+highlight(-8))}}} Multiply the <font color="red">L</font>ast terms:{{{(-8)*(-8)=64}}}.



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So we have the terms: {{{9*z^8}}}, {{{-24*z^4}}}, {{{-24*z^4}}}, and {{{64}}} 



{{{9*z^8-24*z^4-24*z^4+64}}} Now collect every term listed above to make a single expression.



{{{9*z^8-48*z^4+64}}} Now combine like terms.



So {{{(3z^4-8)^2}}} FOILs to {{{9*z^8-48*z^4+64}}}.



In other words, {{{(3z^4-8)^2=9*z^8-48*z^4+64}}}.