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

1 Answer
Aug 13, 2016

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)#.