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Okay. This a perfect square trinomial, or a PST. It factors as (8w+9)^2.
How did you get that?
The way you can tell is because first off, the first and last term are both squares of something. And second off, the middle term is twice the square root of the first and third term. So it's like this.
64w^2 is a square - its root is 8w.
81 is a square - its root is 9.
2*8w*9 is 144w, which is our middle term.
So we know it's a PST. To factor, we take the two roots we have written down, and if the middle term is positive, we use a plus sign. If the middle term is negative, we use a minus sign. And we just write (8w+9)^2. That's it.
Makes sense? Do you want me to go through another example with you?