# How do you factor: [?]

## ${y}^{2} - 6 y + 9$ ? Thanks.

Mar 9, 2018

Two ways to do it. See bellow

#### Explanation:

1st method.

Solve the equeation of second degree

${y}^{2} - 6 y + 9 = 0$. You will obtain 2 roots of this equation, lets say ${a}_{1}$ and ${a}_{2}$...so the factorization will be $\left(y - {a}_{1}\right) \left(y - {a}_{2}\right)$

Second Method. (A little bit more complicated dependeing of given equation. In this case it's easy)

Complete the square

${y}^{2} - 6 y + 9 = {\left(y - 3\right)}^{2} = \left(y - 3\right) \left(y - 3\right)$

Its obvious that prior values ${a}_{1}$ and ${a}_{2}$ are both equal to 3