Solve (3a-4)(2+3a): Binomial Expression Multiplication

To solve this problem, we'll follow these steps:

• Step 1: Apply the distributive property using the FOIL method.
• Step 2: Simplify the expression.
• Step 3: Identify the final simplified polynomial expression.

Now, let’s work through each step:

Step 1: Apply the FOIL method:
(First) Multiply the first terms of each binomial: $3a \cdot 2 = 6a$.
(Outer) Multiply the outer terms: $3a \cdot 3a = 9a^2$.
(Inner) Multiply the inner terms: $-4 \cdot 2 = -8$.
(Last) Multiply the last terms of each binomial: $-4 \cdot 3a = -12a$.

Step 2: Combine the results:
Starting with each term from FOIL: $6a + 9a^2 - 8 - 12a$.
Simplify by combining like terms: $9a^2 + (6a - 12a) - 8 = 9a^2 - 6a - 8$.

Step 3: Identify the resulting polynomial expression:
The expression simplifies to $9a^2 - 6a - 8$.

Therefore, the solution to the problem is $9a^2 - 6a - 8$.