The expression given is:

\[
16(x + 1)^3 + 2
\]

This is already simplified. However, depending on the context, we can expand it if needed. If you'd like to expand it, we can use the binomial theorem or manual expansion. Here's the expanded form:

### Step 1: Expand \((x + 1)^3\)

Using the binomial expansion:
\[
(x + 1)^3 = x^3 + 3x^2 + 3x + 1
\]

### Step 2: Multiply by 16

Now multiply each term by 16:
\[
16(x^3 + 3x^2 + 3x + 1) = 16x^3 + 48x^2 + 48x + 16
\]

### Step 3: Add 2

Now add the 2 to the result:
\[
16x^3 + 48x^2 + 48x + 16 + 2 = 16x^3 + 48x^2 + 48x + 18
\]

So, the expanded form is:

\[
16x^3 + 48x^2 + 48x + 18
\]

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:
1. What is the binomial theorem, and how can it help with expansions?
2. How do you expand powers of binomials in general?
3. How would the expansion change if the exponent was different, say \( (x + 1)^4 \)?
4. What happens if we factor this expression back after expanding it?
5. Can you use this method to expand \( (2x + 3)^3 \)?

**Tip**: When expanding binomials raised to higher powers, writing out the intermediate steps carefully will help avoid mistakes.

Explore the step-by-step expansion of the polynomial expression 16(x + 1)^3 + 2 using the binomial theorem. This algebraic problem demonstrates how to expand binomials and multiply polynomials, ideal for students in Grades 9-11.

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