Question

How do you factor `16-1/4k^2`?

Answer 1

`16-1/4k^2 = (4-1/2k)(4+1/2k)`

Explanation:

The difference of squares identity can be written:

`a^2-b^2 = (a-b)(a+b)`

Note that `16=4^2` and `1/4k^2 = (1/2k)^2` are both perfect squares.

So we find:

`16 - 1/4k^2 = 4^2-(1/2k)^2 = (4-1/2k)(4+1/2k)`