Now that Macbeth has become king he doesn't have to do his own dirty work. His subcontracting the murders of Banquo and Fleance is an indication of his power. Of what use would his status as absolute monarch be if he couldn't delegate such acts? Macbeth probably could have ordered Banquo executed and Fleance along with him on some trumped-up charges, but it was important to him to distance himself from any further killings. When he sees Banquo's ghost sitting in his place at the banquet table in Act 3, Scene 4, the first thing he says is:
Thou canst not say I did it: never shake
Thy gory locks at me.
Shakespeare probably wanted to include a banquet scene in which Banquo's ghost is seated, symbolically, in Macbeth's place of honor. Macbeth does not really know for sure whether Banquo is alive or dead. He only has the assurance of one murderer--and who can believe a murderer when he can't believe his own thanes? If Macbeth had managed to kill Banquo himself, he could not react as strongly to the appearance of the ghost.
Macbeth, of course, would like people to believe he is innocent of Duncan's murder. He wants to achieve a good reputation as a ruler, not unlike Duncan himself. Without a good reputation, his position is insecure.
Besides that, he probably can't imagine killing two people, Banquo and Fleance, without some help. He wouldn't be able to sneak up on them in the dark while they are asleep in his castle. And he could hardly manage to kill both of them while they are out riding on horseback. He knows Banquo strongly suspects him of murdering Duncan and will be on guard. He knows that Banquo has been promised in Act 1, Scene 3:
Thou shalt get kings, though thou be none:
So all hail, Macbeth and Banquo!
Consequently, Banquo, whose prudence Macbeth respects, will anticipate an attempt on his life, since he must understand that the crown is worthless to Macbeth unless he can pass it on to his heirs.
They hail'd him father to a line of kings:
Upon my head they placed a fruitless crown,
And put a barren sceptre in my gripe,
Thence to be wrench'd with an unlineal hand,
No son of mine succeeding. If 't be so,
For Banquo's issue have I filed my mind;
For them the gracious Duncan have I murder'd;
Put rancours in the vessel of my peace
Only for them; and mine eternal jewel
Given to the common enemy of man,
To make them kings, the seed of Banquo kings!
Rather than so, come fate into the list.
And champion me to the utterance! (Act 3, Scene 1)
With Banquo's murder, Macbeth begins his bloody rule. His reputation is in ruins. He did not intend to become a tyrant, but that is what has happened. Since his thanes grow increasingly recalcitrant, he has to become increasingly tyrannical. But this only accelerates his downfall. First Macduff and then others flee to England. He has Macduff's family murdered as a object lesson. This is what will happen to the families of any other turncoats.
In Act 5, Scene 3 he acknowledges that he is all alone, even though he still has some troops who have not deserted him.
Seyton!--I am sick at heart,
When I behold--Seyton, I say!--This push
Will cheer me ever, or disseat me now.
I have lived long enough: my way of life
Is fall'n into the sear, the yellow leaf;
And that which should accompany old age,
As honour, love, obedience, troops of friends,
I must not look to have; but, in their stead,
Curses, not loud but deep, mouth-honour, breath,
Which the poor heart would fain deny, and dare not.