Question

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

Answer 1

You can factor this by grouping.

The coefficients of `x^2` and `y^2` are, respectively, `1` and `9`, the product of which is `9`, which, in turn, can be factored in `(3)(3)`.

So, we can rewrite our function as

`x^2+3xy+9y^2+3xy`

and factor it by two groups of two terms each:

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

We can see that the parenthesis of each term are exactly the same, so we can use them as the common multiple of the whole equation that are multipling the rest:

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

Done!