<s>[INST] Need help simplifiying a rational expression There's a math question on an online test which asks the following
Multiply the following expression, and simplify:
$\frac{x^2-16y^2}{x} * \frac{x^2+4xy}{x-4y}$
But no matter how I try I keep getting the answer incorrect with a message telling me to simplify my answer.  I can't seem to figure out how to simplify it enough to get it right. 
$\frac{x^2-16y^2}{x} * \frac{x^2+4xy}{x-4y}$
 equals, $\frac{x^4 + 4x^3y - 16x^2y^2 - 64xy^3}{x^2-4xy}$. I then factored x out of the numerator and denominator to get $\frac{x(x^3 + 4x^2y - 16xy^2 - 64y^3)}{x(x-4y)}$ and cancelled out the factored x's to get $\frac{x^3 + 4x^2y - 16xy^2 - 64y^3}{x-4y}$.  I don't know what to do from here though.
I've managed to get enough marks to be able to pass it but since it's a readiness test I want to understand all of the material going in.
 [/INST] As mentioned in the comments, by factoring out $x$ in the second fraction, $x^2+4xy$ becomes $x(x+4y)$. Which leaves you with:
$$\frac{x^2+16y^2}{x} \cdot \frac{x(x+4y)}{x-4y}=\frac{(x^2+16y^2)(x+4y)}{x-4y}$$
Alternately if you had not seen the cancellations and had ended up with $x^3+16xy^2+4x^2y+64y^3$ as your numerator. Grouping $x^3+4x^2y$ and $16xy^2+64y^3$ together, notice that $x^2$ and $16y^2$ are common (respectively). Factor them out to get, 
$$x^2(x+4y) + 16y^2(x+4y) = (x^2+16y^2)(x+4y)$$
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