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We are tasked with expanding and simplifying the expression:

\[
(2x + 5)(5x - 3)(3x - 4)
\]

to give an expression of the form \( ax^3 + bx^2 + cx + d \). Let's go step-by-step:

### Step 1: Expand the first two factors
We first expand \( (2x + 5)(5x - 3) \) using distributive property (FOIL method):

\[
(2x + 5)(5x - 3) = 2x(5x) + 2x(-3) + 5(5x) + 5(-3)
\]
\[
= 10x^2 - 6x + 25x - 15
\]
\[
= 10x^2 + 19x - 15
\]

### Step 2: Multiply the result by the third factor
Now, we multiply \( (10x^2 + 19x - 15) \) by \( (3x - 4) \):

\[
(10x^2 + 19x - 15)(3x - 4)
\]

We'll expand this expression term by term:

- \( 10x^2 \times 3x = 30x^3 \)
- \( 10x^2 \times -4 = -40x^2 \)
- \( 19x \times 3x = 57x^2 \)
- \( 19x \times -4 = -76x \)
- \( -15 \times 3x = -45x \)
- \( -15 \times -4 = 60 \)

### Step 3: Combine like terms
Now we combine the terms:

\[
30x^3 + (-40x^2 + 57x^2) + (-76x - 45x) + 60
\]
\[
= 30x^3 + 17x^2 - 121x + 60
\]

### Final Answer:
The expression is now in the form \( ax^3 + bx^2 + cx + d \), where:

- \( a = 30 \)
- \( b = 17 \)
- \( c = -121 \)
- \( d = 60 \)

Let me know if you'd like further clarification or details on any step!

Here are some related questions:
1. What is the process for expanding products of more than two binomials?
2. Can you expand other polynomials like \( (x+1)(x-2)(x+3) \)?
3. How do you use the FOIL method for more complex expressions?
4. Why is it important to combine like terms after expansion?
5. What happens if one factor of the polynomial is a trinomial instead of a binomial?

**Tip:** When expanding multiple binomials, break it down by expanding two at a time before continuing to the next factor.

(2x + 5)(5x - 3)(3x - 4) can be expanded and simplified to give an expression of the form ax^3 + bx^2 + cx + d. Work out the values of a, b, c, and d.

Learn how to expand and simplify the polynomial expression (2x + 5)(5x - 3)(3x - 4) step by step. This problem demonstrates the distributive property and FOIL method, providing the values of a, b, c, and d in the final form ax^3 + bx^2 + cx + d. Suitable for Grades 9-12.

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