apologies, apologize

Apologies or apologies ( rhymes with sees ) is the plural ( more than one ) form of "apology", meaning an expression of regret for an offense or for a lack--
The management extends its apologies to the audience for the show's late start.
We offer our apologies for the inconvenience.

Apologize or apologize ( rhymes with size ) is a verb ( action word ), meaning to offer an expression of regret for a fault or lack--
We forgot to return their call. We should apologize.
That wasn't nice! Apologize to your sister!

Now that you know that, you can say--
"It has taken them so long to apologize, that apologies are in order for the delay, as well as for the original offense."

Note--"apologizes" is the third person singular ( he, she, it ) form of "apologize", meaning to express regret for a fault or lack--
He always apologizes when he has behaved badly.