$(1-t^2)^2 = 1-2t^2 + t^4$ . Why $+ t^4$?

Question

Understand that involution means to multiply value with the same value so many times as involution number. So, understand that $1*1=1$

$t^2 * t^2$ would be 2t^2 (sorry, now understand that this is incorrect. Should be $t^{(2+2)}$ because rule is that for multiplication must sum the exponents).

So far understand.

But why $+ t^4$?

What the rule determines that need $+ t^4$?

If instead t use some number, then yes, all is correct. Just want to understand why $+ t^4$?

What would need to do if, for example $(1-t^2)^4$ or $(1-t^3)^2$ ?

Here is link to "textbook" https://estudijas.rtu.lv/pluginfile.php/287370/mod_resource/content/0/Uzdevumi/Uzdevumi_1.pdf The first page, the first example (1. piemērs. Aprēķināt / 1.example. Must calculate)

Answer 1

By the binomial formula we have $(1-t^2)^2=1-2 \times t^2+{(t^2)}^2=1-2t^2+t^{2 \times 2}=1-2t^2+t^4$.