a) $$ (2 p-3 q)(p-q)(p+q)\left(4 p^{2}+6 p q+9 q^{2}\right) $$

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To expand and simplify the expression:

$$
(2p - 3q)(p - q)(p + q)\left(4p^{2} + 6pq + 9q^{2}\right)
$$

Let's follow these steps:

### Step 1: Simplify $$(p - q)(p + q)$$
$$
(p - q)(p + q) = p^2 - q^2
$$

### Step 2: Multiply by $$(2p - 3q)$$
Now the expression becomes:
$$
(2p - 3q)(p^2 - q^2)\left(4p^{2} + 6pq + 9q^{2}\right)
$$

### Step 3: Recognize Patterns for Further Simplification
Notice that $$4p^2 + 6pq + 9q^2$$ is closely related to the expansion of $$(2p + 3q)^2$$:
$$
(2p + 3q)^2 = 4p^2 + 12pq + 9q^2
$$
However, this doesn't directly factor into our expression.

Instead, observe that the entire expression can be further factored by recognizing it as part of a difference of cubes:
$$
8p^3 - 27q^3 = (2p)^3 - (3q)^3 = (2p - 3q)(4p^2 + 6pq + 9q^2)
$$
So the original expression can be rewritten as:
$$
(p - q)(8p^3 - 27q^3)
$$

### Step 4: Expand the Expression Fully
To present the expression in its expanded form:
$$
(p - q)(8p^3 - 27q^3) = 8p^4 - 8p^3q - 27pq^3 + 27q^4
$$

### Final Answer
$$
8p^{4} - 8p^{3}q - 27p q^{3} + 27q^{4}
$$
The expanded form of the expression is $$8p^{4} - 8p^{3}q - 27p q^{3} + 27q^{4}$$.

a) \( (2 p-3 q)(p-q)(p+q)\left(4 p^{2}+6 p q+9 q^{2}\right) \)

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