Question 186371
In this problem, I'll be using the difference of squares formula, which is:


{{{A^2-B^2=(A+B)(A-B)}}}




{{{a^4-16}}} Start with the given expression.



{{{(a^2)^2-4^2}}} Rewrite {{{a^4}}} as {{{(a^2)^2}}}. Rewrite {{{16}}} as {{{4^2}}}



{{{(a^2+4)(a^2-4)}}} Use the difference of squares formula to factor.



{{{(a^2+4)(a^2-2^2)}}} Rewrite {{{a^4}}} as {{{(a^2)^2}}}. 



{{{(a^2+4)(a+2)(a-2)}}} Use the difference of squares formula to factor.




So {{{a^4-16}}} completely factors to {{{(a^2+4)(a+2)(a-2)}}}