Question

How do you factor a "perfect square trinomial" `16x^2+48x+36`?

Answer 1

First, you can divide by a common factor, which is 4 here.

`= 4x^2 + 12x + 9`

Then factor like normal, but it's just a little harder since it's not `x^2` but `4x^2`. You have either `2x*2x` or `4x*x`. But you said it's a "perfect square trinomial", so it must be `2x*2x`.

`= (2x+3)(2x+3)`

Then multiply by 4 again to return to the original.

`= 4(2x+3)(2x+3) = 4(2x+3)^2`