Having same term in both sides of expression in asymptotic analysis

Question

I am confused if the same terms in both sides cancel each-other, Like in b,c and d ? Any answer would be useful. Thanks in advance

Answer 1

$A(n) = B(n) + \Omega(n)$ means exactly the same thing as $A(n)-B(n) = \Omega(n)$ (and similarly for $o$, $\omega$, $\Theta$ etc).