Question

How do you factor the trinomial `m^2 + 2/3m + 1/9`?

Answer 1

`m^2+2/3m+1/9 = (m+1/3)^2`

Explanation:

This is a perfect square trinomial:

Note that `m^2` and `1/9 = (1/3)^2` are both perfect squares. So the remaining question is whether the middle term matches when you square `(m+1/3)`...

`(m+1/3)^2 = m^2+2(m)(1/3)+(1/3)^2 = m^2+2/3m+1/9`