Factorize: x² - 9.

**The reasoning** You're looking at a **difference of two squares**: a² − b². This special pattern always factorizes as (a − b)(a + b). Here, x² − 9 can be rewritten as x² − 3², where a = x and b = 3. Apply the formula: x² − 3² = (x − 3)(x + 3) To verify: expand (x − 3)(x + 3) = x² + 3x − 3x − 9 = x² − 9 ✓ **Why the wrong options tempt you** - **(x−3)²** expands to x² − 6x + 9, not x² − 9. Students see "−3" and think squaring gives the answer. - **(x+3)²** gives x² + 6x + 9. Same trap — squaring one bracket doesn't work here. - **(x−9)(x+1)** expands to x² − 8x − 9. This looks tempting because you see "9" in the bracket, but the pattern is wrong. **Quick takeaway** When you see **something² minus something²**, think: difference of two squares → (first − second)(first + second). The signs are always opposite!