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The given expression is \((3x + 4)(5x - 2)(4x - 3)\). We need to expand and simplify this expression to find the values of \(a\), \(b\), \(c\), and \(d\) in the form \(ax^3 + bx^2 + cx + d\).

### Step 1: Expand the first two binomials
First, we expand \((3x + 4)(5x - 2)\):

\[
(3x + 4)(5x - 2) = 3x \cdot 5x + 3x \cdot (-2) + 4 \cdot 5x + 4 \cdot (-2)
\]
\[
= 15x^2 - 6x + 20x - 8
\]
\[
= 15x^2 + 14x - 8
\]

### Step 2: Multiply the result with the third binomial
Now, multiply the result \((15x^2 + 14x - 8)\) by \((4x - 3)\):

\[
(15x^2 + 14x - 8)(4x - 3) = 15x^2 \cdot 4x + 15x^2 \cdot (-3) + 14x \cdot 4x + 14x \cdot (-3) + (-8) \cdot 4x + (-8) \cdot (-3)
\]
\[
= 60x^3 - 45x^2 + 56x^2 - 42x - 32x + 24
\]
\[
= 60x^3 + 11x^2 - 74x + 24
\]

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

\[
a = 60, \quad b = 11, \quad c = -74, \quad d = 24
\]

So, the values are:
- \(a = 60\)
- \(b = 11\)
- \(c = -74\)
- \(d = 24\)

Would you like any details or have any questions?

### Relative Questions:
1. How would the process change if one of the binomials was a trinomial?
2. What is the significance of the coefficients in the expanded form?
3. How does expanding binomials help in solving polynomial equations?
4. Can you find the roots of the cubic equation \(60x^3 + 11x^2 - 74x + 24 = 0\)?
5. What methods can be used to factor the final cubic polynomial?

### Tip:
When expanding expressions involving multiple binomials, it's helpful to simplify step-by-step, first handling two binomials at a time before multiplying the result with the next term.

(3x + 4)(5x - 2)(4x - 3) can be expanded and fully 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 (3x + 4)(5x - 2)(4x - 3) to find the coefficients a, b, c, and d in the form ax^3 + bx^2 + cx + d. This problem is ideal for students in Grades 10-12, covering key algebraic concepts.

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