(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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2(x^2 - 8)
It can't be factored because its discriminant is less than zero.
(x - 16)(x + 2) x = 16 or -2
The answer is 4 squared minus 2 squared as 4 squared is 16 minus 2 squared, which is 4, gives you 12 as an answer.
Pull out the common factor of 2 ... 2(y^2+6y-16) Then just factor (y^2+6y-16) ... (y-2)(y+8)