Question

How do you factor `16x^2-1`?

Answer 1

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

Explanation:

Both 16 and 1 are squares. This suggests using the formula for the difference of squares.

Answer 2

`16x^2-1=(4x+1)(4x-1)`

Explanation:

`16x^2-1` is of the form `a^2-b^2` as `16x^2=(4x)^2` and `1^2=1`.

As such it can be factorized as `(a+b)(a-b)` as such

`16x^2-1=(4x)^2-1^2=(4x+1)(4x-1)`

Answer 3

You factor it as a difference of two squares.

Explanation:

Every time you have a difference in the format of

`A^2-B^2` you can factor as `(A-B)(A+B)`.
Then you have to identify if your quantity is the difference of two squared quantities.
It is. In fact we can write it as:

`16x^2-1=(4x)^2-1^2`

Then we can apply our rule

`(4x)^2-1^2=(4x-1)(4x+1)`
and these are your factors.