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Answer 1 · 2018-01-09T22:34:18

#(z^2+4)(z+2)(z-2)=z^4-16#

#z^4-16#

Rewriting:

#(z^2)^2-4^2#

This is the difference of two squares:

#a^2+b^2=(a+b)(a-b)#

Hence:

#(z^2+4)(z^2-4)#

#(z^2-4)=(z^2-2^2)#

Difference of two squares again:

#z^2-2^2=(z+2)(z-2)#

So we have:

#(z^2+4)(z+2)(z-2)=z^4-16#

#(z+2) and (z-2)# are the linear factors.