Stuck On An Integral: (9-3x)^3 - Help!

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The discussion revolves around simplifying the expression (9-3x)^3 in the context of a calculus problem. The user initially seeks help with integrating this expression but later clarifies that they need to simplify it for a longer integral solution. The correct algebraic expansion of (a + b)^3 is confirmed as a^3 + 3a^2b + 3ab^2 + b^3. The substitution method using u=9-3x and its derivative is also mentioned as part of the integral process. Overall, the focus is on algebraic simplification rather than direct integration.
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In the middle of doing an integral for Calc 3, and I came across (9-3x)^3, and completely forgot how to do this from algebra! Help!
 
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Use u=9-3x
du=-3 dx so that -du/3 = dx

so you must really integrate

\int \frac{-1}{3}u^3 du
 
Oh, I guess I didn't phrase my question right, huh? Haha. I'm doing an integral, yes, but I'm not actually taking the integral of that... I just need to simply that part of a loooong answer I got inside an integral... if that makes sense. Just algebra stuff.
 
Is this what it is:

(a + b)^3 = a3 + 3a^2b + 3ab^2 + b^3

?
 
yes that is the expansion of (a+b)^3
 

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