What was the explanation given by Macbeth to the others after he killed the two guards—why does he kill them? After all, who would believe the...

In Shakespeare's Macbeth,
when Macduff arrives to collect King Duncan so that they may continue with Duncan's
travels, pandemonium breaks out when it is realized that Duncan has been murdered.
Macbeth says that when he saw Duncan dead, he lost his head. Who wouldn't?—he
implies.

Here
lay Duncan,

His silver skin laced with his golden
blood,

...who could
refrain,

That had a heart to
love...

Macbeth notes that he
is so overcome by fury that he kills the guards without thinking because he was so
horrified by what "they" had done. The true reason Macbeth kills the guards is so that
they cannot raise suspicion regarding the King's death—they cannot say they heard sounds
in the night or that they felt drugged, etc.

The
guards could raise doubts about how the King actually died, and
this is a concern for Macbeth. He wants nothing to stand in his way of the throne.
Fortuitously, Malcolm and Donalbain flee in fear of their lives. For Macbeth, what could
be better than that he comes straight to the throne because his cousins have run
away?

The only other thing Macbeth needs to be careful of
is Banquo: he is the only person aware of the witches' prophecies for Macbeth, which
would also raise suspicions of Macbeth's involvement, especially in that Duncan died
under Macbeth's roof.