Can this be simplified any furthur? (a^2(a^2-b^2))/(b^2(a-b)

[Hannah]

In my math class right now, we're learning about multiplying rationals, which is basically multiplying fractions with variables in them. I got this as an answer to a question, but I'm not sure if it's simplified all the way:

a²(a²-b²)
b²(a-b)

We don't need to distribute the a² or b². I'm just wondering if you could divide the (a²-b²) by the (a-b)? Is that possible? Is it allowed? And would the quotient be (a+b)? One of the answers on the answer sheet (it's one of those corny Punchline joke worksheets) is:

a²(a+b)
b²

Would that be the simplified answer of my question above, if those two terms were to be divided?

Thanks!

[Martingale]

In my math class right now, we're learning about multiplying rationals, which is basically multiplying fractions with variables in them. I got this as an answer to a question, but I'm not sure if it's simplified all the way:

a²(a²-b²)
b²(a-b)

We don't need to distribute the a² or b². I'm just wondering if you could divide the (a²-b²) by the (a-b)? Is that possible? Is it allowed? And would the quotient be (a+b)? One of the answers on the answer sheet (it's one of those corny Punchline joke worksheets) is:

a²(a+b)
b²

Would that be the simplified answer of my question above, if those two terms were to be divided?

Thanks!