Answer: (x − y).
- A (x + y)
- B (x − y)
- C (x² − y²)
- D (xy)
Correct answer: B. (x − y)
Explanation: xⁿ − yⁿ factors as (x − y)(x<sup>n−1</sup> + ... + y<sup>n−1</sup>), so it is divisible by (x − y).
Mathematical induction works like a row of dominoes: proving the base case P(1) tips the first domino, and proving the inductive step (P(k) ⟹ P(k+1)) guarantees each domino knocks over the next - together these two facts guarantee ALL dominoes fall, without checking each one individually.
Concept context
A proof technique used to establish that a statement is true for every natural number, using a base case and an inductive step.