Why does the distributive property fail when comparing expressions?

As a simplified example, I'm trying to compare whether two expressions are equal, where they are simply written differently. But

syms a x y;
logical((x+y)*a == x*a + y*a)

returns false, and everything else that assumes distributivity of + and *. Is there some other function that will help me, or some explanation why this happens?

[Stephen Prunty]

Ah, just found out apparently using simplify on both sides of the equals returns true.

Answer 1

[Star Strider]

To get logical results with symbolic expressions, use the isAlways (link) function.

syms a x y;
TF = isAlways((x+y)*a == x*a + y*a)

TF =

    logical

     1