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To solve the given problem using the FOIL method, we need to multiply two binomials: 

\[
(8a - 9b)(4a - 3b)
\]

### Applying the FOIL Method
The FOIL method stands for **First, Outer, Inner, Last**:

1. **First**: Multiply the first terms in each binomial:  
   \[
   8a \times 4a = 32a^2
   \]

2. **Outer**: Multiply the outer terms in the binomials:  
   \[
   8a \times (-3b) = -24ab
   \]

3. **Inner**: Multiply the inner terms in the binomials:  
   \[
   -9b \times 4a = -36ab
   \]

4. **Last**: Multiply the last terms in each binomial:  
   \[
   -9b \times (-3b) = 27b^2
   \]

### Combine Like Terms
Now, combine all the terms together:

\[
32a^2 - 24ab - 36ab + 27b^2
\]

Combine the like terms (\(-24ab\) and \(-36ab\)):

\[
32a^2 - 60ab + 27b^2
\]

### Final Answer
The product of the binomials \((8a - 9b)(4a - 3b)\) is:

\[
\boxed{32a^2 - 60ab + 27b^2}
\]

Would you like more details or have any questions about this solution?

### Related Questions:
1. How do you multiply polynomials with more than two terms?
2. What is the distributive property in algebra, and how is it related to the FOIL method?
3. How do you factor a quadratic expression like \(32a^2 - 60ab + 27b^2\)?
4. What are some common mistakes to avoid when using the FOIL method?
5. How do you apply the FOIL method to expressions involving radicals or complex numbers?

**Tip:** Practice the FOIL method with different binomials to get comfortable with recognizing like terms and combining them correctly.

(8a - 9b)(4a - 3b) using the FOIL method to find the product.

Learn how to use the FOIL method to multiply the binomials (8a - 9b)(4a - 3b). This step-by-step solution helps students understand key algebra concepts like the distributive property and combining like terms. Ideal for students in Grades 7-10.

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