During the collision between two balls on the pool table there is no external force along the line of collision between them
Since there is no external force on it so here we can say
[tex]F = 0 = \frac{\Delta P}{\Delta t}[/tex]
here we have
[tex]\Delta P = 0[/tex]
so we can say
[tex]P_i = P_f[/tex]
since there is no external force so we can say during the collision the momentum of two balls will remain conserved