Question

Is `64a^2 - 144ap + 81p^2` a perfect square trinomial, and how do you factor it?

Answer 1

`64a^2 = (8a)^2` and `81p^2 = (9p)^2` or `(-9p)^2`

Noticing the sign of the middle term, we should try:

`(8a-9p)^2` which does indeed work...

`(8a-9p)^2 = (8a)^2-2(8a)(9p)+(9p)^2`

`=64a^2-144ap+9p^2`