Illustration of symbolic variable:

When, on the other hand, z is a symbolic variable to start with, quotes are not required around the expression, and the words are automatically collected:

>> z = sym('z');

>> sym(z^3 + 2*z^3)

ans =

3*z^3

When you want to use the multiple variables as symbolic variable names, the syms function is a shortcut rather than of using sym repetitively. The illustration is as follows,

>> syms x y z

does similar thing as

>> x = sym('x');

>> y = sym('y');

>> z = sym('z');