In Shakespeare's Macbeth, how can I explain Macbeth's murder of Banquo ?

In Shakespeare's Macbeth, after
Macbeth kills Duncan and takes the throne, Macbeth is aware that in order to guarantee
his place as King of Scotland, he must kill Banquo. Even though the
two men are close, their moral compasses are nothing alike. Though Lady Macbeth fears
her husband is not brave enough to take the quickest way to become king, practice makes
perfect, and Macbeth now knows that Banquo must die. He is the only person who was
present to hear the witches' first set of predictions. They also gave Banquo
predictions, but Banquo did not act on them—as Banquo suspects
Macbeth has done. Banquo privately considers Macbeth:

readability="14">

Thou hast it now: King, Cawdor, Glamis,
all,

As the weird women promised, and I
fear

Thou play'dst most foully for't…
 (III.i.1-3)

Macbeth asks
Banquo how far out he will ride, in order to know about what time  he will return, which
he will the murderers he has hired—having convinced them that their misery in life is
Banquo's fault. (Ironically, Macbeth "orders" Banquo not to miss
the feast, even knowing that he will be dead. However, Banquo is true to his word,
showing up as a ghost and reducing Macbeth to a sniveling wretch as opposed to the
powerful man described earlier in the play.)

readability="17">

MACBETH:

...Is't
far you
ride?

BANQUO:

As
far, my lord, as will fill up the time

’Twixt this and
supper. Go not my horse the better,

I must become a
borrower of the night

For a dark hour or
twain.

MACBETH:

Fail
not our
feast.

BANQUO:

My
lord, I will not.
  (III.i.26-32)

Macbeth
realizes that he has risked all to take the throne. After everything he has done, even
sacrificing his immortal soul (because the Elizabethans believed it
was a mortal sin to kill a king), Macbeth realizes that as long as Banquo knows of the
predictions, he will have second thoughts about his Macbeth. Banquo has already told
Macbeth that he will support him as long as he is not asked to do anything
that would compromise his integrity. Macbeth knows that Banquo cannot be
turned "to the dark side." The only solution is to kill his friend. And because the
witches told Banquo that his "issue" (descendants) would be kings,
Macbeth knows that unless he kills Fleance, too, the throne will move into Banquo's
family, as Macbeth has no children. He says that in this case, he has sold his soul
("mine eternal jewel") for someone other than his own
son.

readability="44">

MACBETH:

To
be thus is nothing,

But to be safely thus. Our fears in
Banquo

Stick deep, and in his royalty of
nature

Reigns that which would be fear'd...There is none
but he

Whose being I do fear...He chid the sisters
[and]...

They hail'd him father to a line of
kings:

Upon my head they placed a fruitless
crown

...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
murdered,

...Only for them, and mine eternal
jewel

Given to the common enemy of
man,

To make them kings, the seed of Banquo kings!
(52-74)

This series of events shows us how Macbeth has lost
all touch with the valiant man he was at the play's beginning, compared to Banquo will
not be swayed to follow Macbeth, regardless of the reward—if Macbeth is acting in any
way unsuitable for a king. Macbeth's descent into murder and madness is evident and he
continues to kill in order to maintain his
place.