Question

How do you factor `y^2+6y+9` using the perfect squares formula?

Answer 1

Here's how I go about it.

• Since both the middle and constant terms are positive, it could be a perfect square of the factor `x+c`. The other option is if the middle term is negative but the constant is positive (then the factor is `x-c`).
• The middle term has a coefficient that should be twice the constant if it is to be a perfect square. (That's actually how you'd complete the square.)
• Since half of 6, squared, is 9, the constant term in the factor is half of the middle coefficient in the expanded form.

Though your variable is `y`.

Therefore, this factors into `color(blue)((y+3)^2)`.