What are the 2 ways Pachacuti expanded his empire?strong army & offered protectionAll of thesebought land & foodmade friends & llamas

Pachacuti expanded his empire in two main ways:

1. Strong Army & Offered Protection: Pachacuti built a powerful army to conquer surrounding lands and expand his empire. He also offered protection to those who surrendered without a fight, which encouraged many to join his empire willingly.

2. Diplomacy: While not explicitly mentioned in the options, Pachacuti also used diplomacy to expand his empire. This could involve making alliances, negotiating with other leaders, or offering benefits to those who joined his empire. This is somewhat similar to the option of "making friends".

The options of "bought land & food" and "made friends & llamas" are not typically cited as methods Pachacuti used to expand his empire.