Differential Amplifier.

Differntial amplifier has two gains. 1) Common Mode gain 2) Differential mode gain (For small signals)

Common Mode gain.

The main differential amplifier can be divided into two different  amplifiers as shown above. In order to do that.  The separate Amplifier source resistance(Feedback res)  Rs=2Re. Treat i1 i2 as MOS transistors.
Since Rs acts as feedback resistance.  Rs and RD decides the gain of the above transistor.And gain is almost constant. Increase Rs=2RE. to reject common mode signal.

Differential mode. 

In differential mode, Refer figure 1 (Differential amplifier) .The total current passes through RE resistor.So well defined current multiplied by the resistor=Constant voltage i.e a battery and we can treat is ground.

So in above figure. Vin=vd/2 (one side of total configuration). So Vout=-gm(RL||rds)vd/2 . Let RL=rds.

Then Vout=-gm rds/4 vd. i.e Ad=vout/vd=-gmrds/4...

Important point :In differential amplifier.INCREASE  RE to reject common mode signal.RE doesnt affect differential mode. So Modern designs use Current mirror to increase the resistance RE and provide suitable DC bias for the circuit.