Let's expand the expression \((2x + 3)(x - 4)(x + 5)\).

1. First, we'll expand the first two binomials \((2x + 3)(x - 4)\):
   \[
   (2x + 3)(x - 4) = 2x(x) + 2x(-4) + 3(x) + 3(-4)
   \]
   Simplifying each term:
   \[
   = 2x^2 - 8x + 3x - 12
   \]
   Combining like terms:
   \[
   = 2x^2 - 5x - 12
   \]

2. Now, we'll multiply the result by the third binomial \((x + 5)\):
   \[
   (2x^2 - 5x - 12)(x + 5)
   \]
   Expanding this, we get:
   \[
   = 2x^2(x) + 2x^2(5) - 5x(x) - 5x(5) - 12(x) - 12(5)
   \]
   Simplifying each term:
   \[
   = 2x^3 + 10x^2 - 5x^2 - 25x - 12x - 60
   \]
   Combining like terms:
   \[
   = 2x^3 + 5x^2 - 37x - 60
   \]

So, the expanded form of \((2x + 3)(x - 4)(x + 5)\) is:

\[
\boxed{2x^3 + 5x^2 - 37x - 60}
\]

Would you like further details or have any questions?

Here are 5 related questions you might consider:
1. How would you factor the expression \(2x^3 + 5x^2 - 37x - 60\)?
2. What is the derivative of \(2x^3 + 5x^2 - 37x - 60\) with respect to \(x\)?
3. How would you solve the equation \(2x^3 + 5x^2 - 37x - 60 = 0\)?
4. Can you find the roots of the polynomial \(2x^2 - 5x - 12\) using the quadratic formula?
5. What are the coefficients of each term in the polynomial \(2x^3 + 5x^2 - 37x - 60\)?

**Tip:** When expanding multiple binomials, it's often easier to start by expanding two binomials and then multiplying the result by the remaining expression.

Learn how to expand and simplify the expression (2x + 3)(x - 4)(x + 5) step-by-step with detailed explanations. This problem covers key algebraic concepts including polynomial multiplication and binomial expansion. Suitable for students in Grades 9-12.

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