'Harden' in the Bible

The Lord said to Moses, "When you go back to Egypt, see that you do before Pharaoh all the wonders I have put under your control. But I will harden his heart and he will not let the people go.

But I will harden Pharaoh's heart, and although I will multiply my signs and my wonders in the land of Egypt,

I will harden Pharaoh's heart, and he will chase after them. I will gain honor because of Pharaoh and because of all his army, and the Egyptians will know that I am the Lord." So this is what they did.

And as for me, I am going to harden the hearts of the Egyptians so that they will come after them, that I may be honored because of Pharaoh and his army and his chariots and his horsemen.

If a fellow Israelite from one of your villages in the land that the Lord your God is giving you should be poor, you must not harden your heart or be insensitive to his impoverished condition.

Why harden your hearts like the Egyptians and Pharaoh did? When God treated them harshly, didn't the Egyptians send the Israelites on their way?