$1)(\forall x P(x)) \wedge A \equiv \forall x (P(x) \wedge A)$
Here put boolean variable to get the ans.
$A$ is free variable. So, it's value can be true or false.
Now, putting $A=1$,we will get both side value is equal.
Similarly, putting $A=0,$ Both side will return $0.$
So, above equation is valid.
$2)$ Similar as previous one. It also will be valid