Έχοντας στρώσει το κρεβάτι, τίναξα το πάπλωμα και άνοιξα λίγο το παράθυρο να μπει αέρας.

Having made the bed, I shook out the duvet and opened the window a little to let some air in.

Breakdown of Έχοντας στρώσει το κρεβάτι, τίναξα το πάπλωμα και άνοιξα λίγο το παράθυρο να μπει αέρας.

• και: and
• λίγο: a little
• έχω: to have
• να: to

Questions & Answers about Έχοντας στρώσει το κρεβάτι, τίναξα το πάπλωμα και άνοιξα λίγο το παράθυρο να μπει αέρας.

What does Έχοντας στρώσει το κρεβάτι mean grammatically?

It is a non-finite introductory clause meaning something like having made the bed.

• έχοντας = having
• στρώσει = the participle form used here after έχοντας
• το κρεβάτι = the bed

So the structure έχοντας + participle often corresponds to English having done... or sometimes simply after doing....

In this sentence, it sets up an action that happened before the main actions:

• Having made the bed, I shook the duvet and opened the window a little...

This structure is quite common in written Greek and in more careful speech.

Why is it στρώσει and not στρώνοντας?

Because these two forms express different ideas.

1. έχοντας στρώσει

This means having made the bed / after making the bed.
It suggests the action was completed first.

2. στρώνοντας

This means making the bed / while making the bed.
It usually suggests an action in progress or something happening at the same time.

So:

• Έχοντας στρώσει το κρεβάτι, ... = After I had made the bed, ...
• Στρώνοντας το κρεβάτι, ... = While I was making the bed, ...

In your sentence, the speaker first finished making the bed, and then did the next actions, so έχοντας στρώσει fits better.