Here's a method if you want to do it from scratch. This was my actual thought process for it, hence the unconess of it. There's probably a MUCH better way of doing this but I've avoided using complex numbers altogether in this method to show some algebraic techniques that could even be used in methods (although I doubt you'll ever need to);
^2+8^2)
<---you should know you're after two quadratic factors since it should be obvious they're not linear, and hence, this step involving squares seems the logical way to go
^2+a)
, where a is something in terms of z. The reason for the a is that
^2)
isn't equal to what we had before. I totally changed it around to make it resemble a quadratic, and the a is in there to compensate for any changes. This step seems a bit far fetched, but I guess it just comes with experience.
Next, by expanding our new brackets, we get
. Hence, our a is
to cancel out the term we added in.
Hence,
^2 -16z^2=(z^2+8)^2 -(4z)^2=(z^2-4z+8)(z^2+4z+8))
But yeh, it's obviously best to use complex numbers, find the linear factors, then multiply the conjugate pairs.
EDIT: Mistakes @_@
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