Question

factor y^3+y^2-4x-4 and t^2+4z^2

Answer 1

the first can be done by eyeballing it and grouping:

y^3+y^2 - 4x-4
y^2(y+1) - 4(x+1)
Now, if there's a typo and you meant 4y-4, then you end up with
(y^2-4)(y+1)
(y+2)(y-2)(y+1)

t^2+4z^2
cannot be factored, but
t^2-4z^2 = (t-2z)(t+2z)