When you expand your zoo, you'll be best off keeping it as a square: this maximizes how much space you'll gain for each expansion. In other words, expand to the side, then the back; side, then back.
Expansion costs
1st Expansion $50,000
2nd Expansion $300,000
3rd Expansion 40 Diamonds or $2,500,000
4th Expansion 80 Diamonds
5th Expansion 160 Diamonds
6th Expansion 320 Diamonds
7th Expansion 320 Diamonds or $5,000,000
8th Expansion 320 Diamonds or $12,500,000
9th Expansion 300 Diamonds or $15,000,000
10th Expansion 320 Diamonds
11th Expansion 320 Diamonds or $35,000,000
12th Expansion 320 Diamonds
13th Expansion 320 Diamonds
14th Expansion 320 Diamonds or $70,000,000
15th Expansion 320 Diamonds