Question 174836
This expression represents a difference of squares {{{(a+b)(a-b)=a^2-b^2}}}



So {{{(x^2+16)(x^2-16)=(x^2)^2-(16)^2=x^4-256}}}



====================================================================



Alternative (slightly longer) Explanation:




{{{(x^2+16)(x^2-16)}}} Start with the given expression.



Now let's FOIL the expression.



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



{{{(highlight(x^2)+16)(highlight(x^2)-16)}}} Multiply the <font color="red">F</font>irst terms:{{{(x^2)*(x^2)=x^4}}}.



{{{(highlight(x^2)+16)(x^2+highlight(-16))}}} Multiply the <font color="red">O</font>uter terms:{{{(x^2)*(-16)=-16x^2}}}.



{{{(x^2+highlight(16))(highlight(x^2)-16)}}} Multiply the <font color="red">I</font>nner terms:{{{(16)*(x^2)=16x^2}}}.



{{{(x^2+highlight(16))(x^2+highlight(-16))}}} Multiply the <font color="red">L</font>ast terms:{{{(16)*(-16)=-256}}}.



---------------------------------------------------



{{{x^4-16x^2+16x^2-256}}} Now collect every term to make a single expression.



{{{x^4-256}}} Now combine like terms.



So {{{(x^2+16)(x^2-16)}}} FOILs to {{{x^4-256}}}.



In other words, {{{(x^2+16)(x^2-16)=x^4-256}}}.