Which model can be used to find 99² easily?

Correct answer: The difference-square model for (100 − 1)²

The correct answer is A: use 99² = (100 − 1)². Choose the nearby round number 100 and write 99 as 100 − 1. Applying (a − b)² = a² − 2ab + b² gives 99² = 100² − 2(100)(1) + 1² = 10,000 − 200 + 1 = 9,801. This model is especially convenient because 100² and 2·100 are easy to calculate. Option B is not the useful representation asked for: although 90 + 9 equals 99, the resulting calculation is less convenient and the option does not use the nearest round-number idea. Option C gives (99 + 1)(99 − 1) = 100 × 98 = 9,800, which is 99² − 1, so it is not equal to 99². Option D gives 10,001, not 9,801, because it ignores the cross term. Memory cue: for a number just below a round number, use (N − 1)² = N² − 2N + 1.