Question

How do you factor the expression `1/9x^2 - 1/4`?

Answer 1

Use the difference of squares identity to find:

`1/9x^2-1/4 = (x/3-1/2)(x/3+1/2)`

Explanation:

Both `1/9 x^2 = (x/3)^2` and `1/4 = (1/2)^2` are perfect squares.

So you can conveniently use the difference of squares identity:

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

with `a = x/3` and `b=1/2` to find:

`1/9x^2-1/4 = (x/3)^2-(1/2)^2 = (x/3-1/2)(x/3+1/2)`