SOLUTION: I'm needing some help with the following problem: Factor each completely. Some may require several steps. a^4-16 thanks!

Algebra ->  Equations -> SOLUTION: I'm needing some help with the following problem: Factor each completely. Some may require several steps. a^4-16 thanks!      Log On


   

Question 186371: I'm needing some help with the following problem: Factor each completely. Some may require several steps.
a^4-16
thanks!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
In this problem, I'll be using the difference of squares formula, which is:

A%5E2-B%5E2=%28A%2BB%29%28A-B%29



a%5E4-16 Start with the given expression.


%28a%5E2%29%5E2-4%5E2 Rewrite a%5E4 as %28a%5E2%29%5E2. Rewrite 16 as 4%5E2


%28a%5E2%2B4%29%28a%5E2-4%29 Use the difference of squares formula to factor.


%28a%5E2%2B4%29%28a%5E2-2%5E2%29 Rewrite a%5E4 as %28a%5E2%29%5E2.


%28a%5E2%2B4%29%28a%2B2%29%28a-2%29 Use the difference of squares formula to factor.



So a%5E4-16 completely factors to %28a%5E2%2B4%29%28a%2B2%29%28a-2%29