ab^2+8ab-9a

The given expression is ab^2 + 8ab - 9a.

To solve this expression, you can factor out the common terms if possible. Notice that all terms have a common factor of "a".

Taking out the common factor "a", we get:
a(b^2 + 8b - 9)

Now, we need to factorize the trinomial expression within the parentheses, b^2 + 8b - 9. To do this, we need to find two numbers whose product is equal to the product of the coefficient of b^2 (-1) and the constant term (-9), and whose sum is equal to the coefficient of b (8).

The two numbers that satisfy these conditions are 9 and -1, since 9 * (-1) = -9 and 9 + (-1) = 8.

Now, we can rewrite the expression as follows:
a(b^2 + 9b - 1b - 9)
a(b(b + 9) - 1(b + 9))
a(b - 1)(b + 9)

Therefore, the factored form of the given expression ab^2 + 8ab - 9a is: a(b - 1)(b + 9).