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The image shows the problem:

\[
\text{Multiply } (x + 2)(x^3 - 3x + 4)
\]

Let's solve this by applying the distributive property (also known as the FOIL method when dealing with binomials), where each term in the first expression is multiplied by each term in the second expression:

\[
(x + 2)(x^3 - 3x + 4)
\]

### Step-by-step solution:
1. Multiply \(x\) by each term in \((x^3 - 3x + 4)\):
   \[
   x \cdot x^3 = x^4
   \]
   \[
   x \cdot (-3x) = -3x^2
   \]
   \[
   x \cdot 4 = 4x
   \]

   So, \(x(x^3 - 3x + 4) = x^4 - 3x^2 + 4x\).

2. Multiply \(2\) by each term in \((x^3 - 3x + 4)\):
   \[
   2 \cdot x^3 = 2x^3
   \]
   \[
   2 \cdot (-3x) = -6x
   \]
   \[
   2 \cdot 4 = 8
   \]

   So, \(2(x^3 - 3x + 4) = 2x^3 - 6x + 8\).

3. Now, combine the results from both steps:
   \[
   (x + 2)(x^3 - 3x + 4) = x^4 - 3x^2 + 4x + 2x^3 - 6x + 8
   \]

4. Simplify by combining like terms:
   \[
   = x^4 + 2x^3 - 3x^2 - 2x + 8
   \]

The final answer is:
\[
x^4 + 2x^3 - 3x^2 - 2x + 8
\]

Would you like further clarification on any part of this solution?

Here are 5 related questions for deeper exploration:
1. How would you multiply two polynomials of higher degrees?
2. What is the distributive property and how does it work with polynomials?
3. Can you multiply more than two polynomials at once?
4. How does this method change if one factor is a trinomial instead of a binomial?
5. What is the role of combining like terms after polynomial multiplication?

**Tip:** Always ensure you correctly distribute each term and combine like terms to simplify the final result.

Multiply the polynomials (x + 2)(x^3 - 3x + 4).

Learn how to multiply polynomials using the distributive property with the example (x + 2)(x^3 - 3x + 4). This guide provides a step-by-step solution, demonstrating each multiplication and combination of like terms.

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