h^{2 }-9hs+9s^{2}

Jessica,

The polynomial h^{2}-9hs+9s^{2} cannot be factored out to anything simpler. However, if there is a typo and the polynomial is supposed to read h^{2}-6hs+9s^{2} then you can factor it be remembering F.O.I.L. (First, Outside, Inside, Last) and performing it in reverse.

So, to get the h^{2}, the two factors must begin with "h". Then to get the last part "+9s^{2}, both factors must end with + or - 3s. And because the middle part is a negative 9hs, it means that the 3s must have a negative sign. So the two factors are (h-3s) (h-3s), or (h-3s)^{2} in complete factorization.

Performing F.O.I.L. on this gives h^{2}-3hs-3hs+9s^{2}, or h^{2}-6hs+9s^{2}.