How do you Factor t^2 + 4z^2

you can't in general, using real numbers.

t^2+4z^2 = (t+2zi)(t-2zi)

If you have a typo and meant

t^2 - 4z^2, that is (t-2z)(t+2z)

y^3+y^2-4y-4

To factor the expression t^2 + 4z^2, we need to look for any common factors between the terms. In this case, we cannot factor out any common factors because t^2 and 4z^2 have different variables.

However, t^2 + 4z^2 is a special type of expression called a sum of squares. There is a formula called the difference of squares that can be used to factor such expressions. The difference of squares formula states that a^2 - b^2 can be factored as (a + b)(a - b).

We can rewrite t^2 + 4z^2 as (t)^2 + (2z)^2 to identify it as a sum of squares. Using the difference of squares formula, we can express t^2 + 4z^2 as follows:

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

So, the factored form of t^2 + 4z^2 is (t + 2z)(t - 2z).