At various times one or the other will extend the hand out but it will be pushed back.

Is it extreme to extend the hand of friendship to those in flight from persecution?

When two people meet, one will extend a hand while the other offers an elbow.

In more expansive mood, 'extend a hand' might have been the 'yes we can' of this speech.

We like to see a footballer extend a hand to help a fallen opponent to his feet.