Factorize x² − 9.

**The reasoning** You're looking at a **difference of two squares**: x² − 9. Notice that 9 = 3², so you can rewrite this as: x² − 3² There's a beautiful formula for this pattern: **a² − b² = (a − b)(a + b)** Here, a = x and b = 3, so: x² − 9 = x² − 3² = (x − 3)(x + 3) You can verify: expand (x − 3)(x + 3) and you get x² + 3x − 3x − 9 = x² − 9 ✓ **Why the wrong options tempt you** - **A & C** look familiar because of the ±3, but squaring (x−3)² gives you x² − 6x + 9, not x² − 9. Perfect squares always have that middle term! - **D** is random—multiplying it out gives x² − 8x − 9, totally different. **Quick takeaway** Whenever you see **something² minus something²**, think *difference of two squares* and split it into **(first − second)(first + second)**—the middle terms will always cancel perfectly.