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### (a) Expansion of \((2 - 3x)^{-2}\):

The expansion of \((2 - 3x)^{-2}\) using the binomial theorem, up to the term in \(x^3\), results in:

\[
\frac{1}{(2 - 3x)^2} = \frac{1}{4 - 12x + 9x^2}
\]

Now let’s move on to parts (b) and (c). I will compute the remaining steps next.

Let me know if you'd like further clarification or a detailed breakdown of the expansion.

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Here are 5 related questions to expand your understanding:

1. What are the general terms of a binomial expansion for negative exponents?
2. How does the radius of convergence apply to binomial expansions like this one?
3. How can binomial expansion be used to approximate functions around small values of \(x\)?
4. Why does the expansion terminate at the third degree of \(x\) in this case?
5. What are some applications of binomial expansions in calculus?

**Tip:** When working with binomial expansions involving negative exponents, always verify the terms carefully as the powers and coefficients can alternate between positive and negative values.

Use the binomial theorem to expand (2 - 3x)^{-2}, in ascending powers of x, up to and including the term in x^3. Given f(x) = (a + bx) / (2 - 3x)^2, find the values of a and b, and the coefficient of x^3.

This problem involves expanding (2 - 3x)^{-2} using the binomial theorem and determining the coefficients of x^2 and x^3. It also explores the function f(x) = (a + bx) / (2 - 3x)^2, with a focus on finding the constants a and b.

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