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The expression provided is \((2x + 1)(x^2 + 5x - 3)\).

To solve this, we will apply the distributive property (also known as the FOIL method for binomials). Here's the step-by-step expansion:

1. First, distribute \(2x\) across all the terms in the second factor \((x^2 + 5x - 3)\):
   \[
   2x \cdot (x^2 + 5x - 3) = 2x^3 + 10x^2 - 6x
   \]

2. Next, distribute \(1\) across all the terms in the second factor:
   \[
   1 \cdot (x^2 + 5x - 3) = x^2 + 5x - 3
   \]

3. Now, combine all terms:
   \[
   2x^3 + 10x^2 - 6x + x^2 + 5x - 3
   \]

4. Combine like terms:
   \[
   2x^3 + (10x^2 + x^2) + (-6x + 5x) - 3 = 2x^3 + 11x^2 - x - 3
   \]

So, the fully expanded form of \((2x + 1)(x^2 + 5x - 3)\) is:
\[
\boxed{2x^3 + 11x^2 - x - 3}
\]

Would you like further details or have any questions about this process?

Here are five related questions to deepen your understanding:
1. How does the distributive property work in polynomial multiplication?
2. What is the FOIL method, and when is it typically used?
3. Can you explain how to combine like terms in an algebraic expression?
4. How would you solve this equation if it were set equal to zero?
5. How does polynomial multiplication relate to factoring polynomials?

**Tip:** Always organize your terms carefully when combining them to avoid mistakes in polynomial expansions.

Learn how to expand the polynomial expression (2x + 1)(x^2 + 5x - 3) using the distributive property. This problem covers key algebraic concepts, including polynomial multiplication and combining like terms. Suitable for students in Grades 9-11.

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