a^2b^2-2a^2b-15a^2

To simplify the expression a^2b^2 - 2a^2b - 15a^2, we need to factor out the common terms, if any.

The expression has three terms: a^2b^2, -2a^2b, and -15a^2.

First, let's look for any common factors among the three terms. We can see that each term has a common factor of a^2. So, we can factor out a^2 from each term.

Factoring out a^2, we get:

a^2b^2 - 2a^2b - 15a^2 = a^2(b^2 - 2b - 15)

Now, we have simplified the expression by factoring out the common factor a^2. The expression is now in its simplest form.

If you want to further simplify, you can factor the quadratic expression b^2 - 2b - 15. To factor this quadratic expression, we need to find two numbers whose product is -15 and whose sum is -2.

By trial and error or by using the quadratic formula, we find that the numbers are -5 and 3.

So, b^2 - 2b - 15 can be factored as (b - 5)(b + 3).

Plugging this back into the simplified expression, we have:

a^2(b^2 - 2b - 15) = a^2(b - 5)(b + 3)

Therefore, the fully simplified expression is a^2(b - 5)(b + 3).