## Explanation

### Simplify the Problem

To solve $(3n \pm 5)2n$, we first need to understand the form and notation of the expression. It seems that we are handling two possible cases:

$(3n + 5)2n$ $(3n - 5)2n$### General Approach

For either case, we'll evaluate the expression by breaking it down step-by-step.

### Case 1: $(3n + 5)2n$

We need to simplify $(3n + 5) \times 2n$:

$(3n + 5)2n = 3n \cdot 2n + 5 \cdot 2n$**Simplify further**:

### Case 2: $(3n - 5)2n$

Similarly, we evaluate $(3n - 5) \times 2n$:

$(3n - 5)2n = 3n \cdot 2n - 5 \cdot 2n$**Simplify further**:

### Final Result

To summarize the simplified forms of both cases:

$\begin{cases} (3n + 5)2n = 6n^2 + 10n \\ (3n - 5)2n = 6n^2 - 10n \end{cases}$In either scenario, the expression reduces to a **quadratic polynomial**. Understanding these steps will allow you to solve similar expressions effectively.