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!