Prove and use polynomial identities

What you'll learn

1. Distinguish a polynomial identity (true for all values) from a polynomial equation (true for specific values), and justify the distinction
2. Prove polynomial identities by expanding both sides and showing they are equal, or by algebraically transforming one side to match the other
3. Apply the standard polynomial identities (difference of squares, sum/difference of cubes, and the given Pythagorean-triple identity) to simplify or verify expressions
4. Use the Pythagorean-triple identity (x² + y²)² = (x² - y²)² + (2xy)² to generate Pythagorean triples by substituting specific integer values
5. Explain how a polynomial identity creates an infinite family of numerical relationships