Question

How do you factor `x^2 + 6x + 9`?

Answer 1

`color(green)((x+3)(x + 3)`

Explanation:

`x^2+6x+9`

We can Split the Middle Term of this expression to factorise it
In this technique, if we have to factorise an expression like `ax^2 + b + c`, we need to think of 2 numbers such that:

`N_1*N_2 = a*c = 1* 9 = 9`
AND
`N_1 +N_2 = b = 6`
After trying out a few numbers we get `N_1 = 3` and `N_2 =3`
`3*3 = 9`, and `3+3= 6`

`x^2+6x+9`
`=x^2+3x + 3x+9`

`=x(x + 3) + 3(x+3)`

`=color(green)((x+3)(x + 3)`