In Shakespeare's play Macbeth, how does the title character attempt to cover up his treachery?

In Shakespeare’s play Macbeth, the
title character begins to attempt to cover up his murder of the king very quickly after
the murder is committed.  Significantly, however, it is his wife, Lady Macbeth, who is
the first to suggest practical action.  She is often the instigator of actions in the
first half of the play, and it was she, of course, who urged her husband to murder the
king in the first place.  Therefore it seems fitting that she should also be the one who
initially takes the lead in attempting to cover up the crime.  Thus she tells her
husband (in the “Open Source Shakespeare” edition of the play
[www.opensourceshakespeare.org]):

readability="8">

. . . Go get some water,
And wash this
filthy witness from your hand.
Why did you bring these daggers from the
place?
They must lie there: go carry them; and smear
The sleepy
grooms with blood. 
(706-10)

Of course, the play
will subsequently show that responsibility for the crime cannot be hidden as easily as
this, either from others or from Macbeth.

Unsurprisingly,
it is Lady Macbeth who once again takes the initiative when her husband seems to
falter:

. . .
Infirm of purpose!
Give me the daggers: the sleeping and the
dead
Are but as pictures: 'tis the eye of childhood
That fears a
painted devil. If he do bleed,
I'll gild the faces of the grooms withal;

For it must seem their guilt.
(714-19)

When Macbeth again
seems to regret what he has done, Lady Macbeth once more speaks with an authority and
self-assurance that later prove extremely ironic:

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A little water clears us of this deed:

How easy is it, then! Your constancy
Hath left you unattended.
(734-36)

A few seconds later,
she again instructs her husband, this time advising him to change his
clothing:

Get
on your nightgown, lest occasion call us,
And show us to be watchers. Be not
lost
So poorly in your thoughts.
(739-41)

Later, Macbeth
pretends as if nothing has happened when a visitor comes calling for the
king:

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Macduff. Is the
king stirring, worthy thane?

Macbeth.
Not yet.

Macduff.
He did command me to call timely on him:

I
have almost slipp'd the hour.

Macbeth.
I'll bring you to him.
(809-13)

Almost immediately
after killing the king, then, Macbeth and his wife must undertake a task far more
difficult than committing the crime itself: attempting to distance themselves from being
suspected of the murder.