Is It Always True?

Identities and counterexamples

An interactive lesson with 7 steps, about 6 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• An identity holds for every value; one counterexample disproves a claim.
• Testing values can disprove; only algebra proves for all values.
• Classic false friends: (a + b)² ≠ a² + b², √(a² + b²) ≠ a + b.

Steps

1. Identities and equations
2. Graphs of both sides
3. Spot the identities
4. Roots don’t split
5. Repair the claim
6. When does the wrong formula work?
7. An identity in disguise