Find the binomial expansion of x2(x-2y)3. 2. Find the term independent of x in the expansion of (x - (3)/(x))4. 3. Find the first three terms in ascending powers of y in the expansion of (1-y)^(1)/(3)

Here $a=x$, $b=-2y$, $n=3$.

The final answer is $\boxed{x^5 - 6x^4y + 12x^3y^2 - 8x^2y^3}$.

2. Find the term independent of $x$ in the expansion of $\left(x - \frac{3}{x}\right)^4$.

Here $a=x$, $b=-\frac{3}{x}$, $n=4$.

The final answer is $\boxed{54}$.

3. Find the first three terms in ascending powers of $y$ in the expansion of $(1-y)^{\frac{1}{3}}$.

Use the binomial expansion for fractional powers: $(1+x)^n = 1 + nx + \frac{n(n-1)}{2!}x^2 + \dots$
Here $x=-y$ and $n=\frac{1}{3}$.

The first three terms are $\boxed{1 - \frac{1}{3}y - \frac{1}{9}y^2}$.

4. Find the coefficient of $x^{-3}$ in the expansion of $\left((x+1)\left(2x - \frac{1}{x}\right)^3\right)$.

Let $a=2x$ and $b=-\frac{1}{x}$.

The term with $x^{-3}$ is $-x^{-3}$.
The coefficient of $x^{-3}$ is $-1$.
The final answer is $\boxed{-1}$.