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(4x + 1)(4x - 1)

You can think of this like any other factoring problem.

16x2 - 1 is just like 16x2-0x -1, which shows you that the two terms that just have x in them cancel each other out. That means that they have the same coefficient, and opposite signs.

So looking at 16, it can be split into 4 and 4. These are the front coefficients of each section. Then, you know that to get a negative one, you have to have a positive one in one chunk, and a negative one in the other. Then, when you foil it out, the term with a single x is gone, and you prove that the answer is right.

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