The sum of momentum of two objects before collision and sum of momentum of two objects after collision are equal.

let A and B be any objects
initial velocity of A =u1
initial velocity of B = u2
let mass of A be m1
let mass of B e m2
let both the objects collide after some time and collision lasts for t seconds 
let the velocity of A after collision =v1
let the velocity of B after collision =v2
momentum =mass *velocity
momentum of A before collision =m1*u1
momentum of B before collision = m2*u2
momentum of A after collision = m1*v1
momentum of B after collision = m2*v2
now we know the rate of change of momentum  =mass *rate of  change in velocity =mass*change in velocity /time
rate of  change of momentum of A during collision ,FAB =m1(v1-u1)/t
rate of change of momentum of B during collision, FBA  =m2 (v2-u2)/t
m1(v1-u1)/t = -m2 (v2 -u2)/t
m1(v1-u1) = -m2(v2-u2)
m1v1-m1u1 = -m2v2+m2u2
m1v1+m2v2 = m1u1+m2u2
m1u1+m2u2 = m1v1+m2v2

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law of conservation of momentum states that if two or more bodies collides there total momentum after collision is always equal to the total momentum before collision unless an unbalanced force does not acts on them.

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