How do you factor 1/49 - x^2?

1 Answer
Mar 5, 2018

(1/49 - x^2) =
(1/7 + x) * (1/7 - x )

Explanation:

1/49 is the same as (1^2/7^2). 1/49 and x^2 are both perfect squares so we use the difference of squares (factoring).
(a^2 - b^2) = (a + b) * (a - b)
If you 'foil' the answer, you get (a^2 - ab +ab - b^2). (-ab) and (+ab) cancel, resulting in the original (a^2 - b^2).
For the problem, the same process applies:
1. (1/49 - x^2)
2. (1/7 + x) * (1/7 - x )
To check, [(1/7 * 1/7) - (1/7)x + (1/7)x - (x*x)] = (1/49 - x^2)