A) [tex] \sum_{r=0}^{2} { 2 \choose r} (x^2)^{2-r}[/tex]
$=\boxed{ x^4+2x^2+1}$
B) Associativity property of addition.
C) Applying Binomial theorem to the expression yields $x^4+2x^2+1$
D) [...] using the Associativity property of addition.
