You're right - that answer explanation does nothing to help you figure out *how* to get to the difference of squares solution. OG answer explanations are by nature succinct, and not always the most helpful.

You know that you definitely don't want to calculate 3x3x3x3x3x3x3x3, then subtract 2x2x2x2x2x2x2x2, then factor. There's no way to get there in 2 minutes! So, what are the clues from the problem that difference-of-squares was the right approach? The biggest clue is the word FACTOR. If the question is asking you which of the following is not a factor, then that must mean that the rest of the answer choices are factors.

If you were given a single number or term, and asked about its factors, you could use a factor tree to break it down. Here, though, we're given a difference of two terms: 3^8 and 2^8. There's no way to combine the terms simply by combining the exponents or anything like that. Since you know that there has to be a trick/shortcut involved, look at the structure. You may not have seen questions involving something to the 8th power before, but the structure x^a - y^a should look familiar.

In fact, any time you see the structure [something to an exponent] - [something to an exponent], you should ask yourself if it could be a difference of squares. It often is.

Here are just a few examples of hidden difference-of-squares problems that I've seen:

1 - a^4

4x^2 - 9

-m^6 + n^12

n^3 - n (when we factor this one, we see that it turns into the product of 3 consecutive integers)

The best way to recognize it in the future is just to make a note of every example that you see of the rule, and ask yourself what connects them.