We were given;
[tex]y^4 -16[/tex] to factor over the complex numbers.
We can rewrite the given expression to look like difference of two squares,
[tex]y^4 -16=(y^2)^{2} -4^2[/tex]
[tex]y^4 -16=(y^2+4)(y^2-4)[/tex]
[tex]y^4 -16=(y^2--4)(y^2-4)[/tex]
We can still rewrite as,
[tex]y^4 -16=(y^2--2^2)(y^2-2^2)[/tex]
We can still rewrite as
[tex]y^4 -16=(y^2-2^2\times-1)(y^2-2^2)[/tex]
[tex]y^4 -16=(y^2-2^2(-1))(y^2-2^2)[/tex]
Applying difference of two squares again, we have;
[tex]y^4 -16=(y+2\sqrt{-1})(y-2\sqrt{-1})(y+2)(y-2)[/tex]
Note that, in complex numbers
[tex]\sqrt{-1}=i[/tex]
[tex]y^4 -16=(y+2i)(y-2i)(y+2)(y-2)[/tex]
