Find each of the following products :
`(2x + 5) xx (4x - 3)`

Answer

To find the product of the algebraic expressions \( (2x + 5) \) and \( (4x - 3) \), we will use the distributive property (also known as the FOIL method for binomials). Here are the steps to solve the problem:

### Step-by-Step Solution:

1. **Write down the expression**:
\[ (2x + 5)(4x - 3) \]

2. **Distribute each term in the first bracket to each term in the second bracket**:
- First, multiply \( 2x \) by both terms in the second bracket:
\[ 2x \cdot 4x + 2x \cdot (-3) \]
- Then, multiply \( 5 \) by both terms in the second bracket:
\[ 5 \cdot 4x + 5 \cdot (-3) \]

3. **Calculate each multiplication**:
- From \( 2x \cdot 4x \):
\[ 2 \cdot 4 = 8 \quad \text{and} \quad x \cdot x = x^2 \quad \Rightarrow \quad 2x \cdot 4x = 8x^2 \]
- From \( 2x \cdot (-3) \):
\[ 2 \cdot (-3) = -6 \quad \Rightarrow \quad 2x \cdot (-3) = -6x \]
- From \( 5 \cdot 4x \):
\[ 5 \cdot 4 = 20 \quad \Rightarrow \quad 5 \cdot 4x = 20x \]
- From \( 5 \cdot (-3) \):
\[ 5 \cdot (-3) = -15 \quad \Rightarrow \quad 5 \cdot (-3) = -15 \]

4. **Combine all the results**:
\[ 8x^2 - 6x + 20x - 15 \]

5. **Combine like terms**:
- Combine the \( x \) terms:
\[ -6x + 20x = 14x \]
- So, the expression simplifies to:
\[ 8x^2 + 14x - 15 \]

### Final Answer:
\[ 8x^2 + 14x - 15 \]