To simplify the expression \((3a - 4)(2a + 1)\), follow these steps:

1. **Apply the distributive property** (also known as FOIL for binomials):
   \[
   (3a - 4)(2a + 1) = 3a(2a + 1) - 4(2a + 1)
   \]

2. **Distribute each term**:
   - \(3a \times 2a = 6a^2\)
   - \(3a \times 1 = 3a\)
   - \(-4 \times 2a = -8a\)
   - \(-4 \times 1 = -4\)

3. **Combine all the terms**:
   \[
   6a^2 + 3a - 8a - 4
   \]

4. **Simplify like terms**:
   \[
   6a^2 - 5a - 4
   \]

Thus, the simplified expression is:
\[
6a^2 - 5a - 4
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How would you solve \((5a + 2)(a - 3)\)?
2. What happens if we factor \((6a^2 - 5a - 4)\) back into two binomials?
3. Can you expand and simplify \((4a - 5)(3a + 7)\)?
4. How do you solve \((x + 3)(x - 4) = 0\)?
5. How do you use the distributive property to multiply three binomials?

**Tip:** Always combine like terms carefully to ensure accurate simplification!

Learn how to simplify the expression (3a - 4)(2a + 1) using the distributive property (binomial expansion). This problem involves key algebraic concepts such as expanding and combining like terms, making it suitable for students in Grades 7-9.

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