Let's expand the expression $(4b - 4)(3b - 4)$.

To do this, we'll use the distributive property (also known as FOIL for binomials):

$(4b - 4)(3b - 4) = 4b(3b) + 4b(-4) + (-4)(3b) + (-4)(-4)$

Now, we'll simplify each term:

1. $4b \times 3b = 12b^2$
2. $4b \times -4 = -16b$
3. $-4 \times 3b = -12b$
4. $-4 \times -4 = 16$

So, combining all the terms together:

$12b^2 - 16b - 12b + 16$

Now, combine like terms:

$12b^2 - 28b + 16$

Thus, the expanded form of $(4b - 4)(3b - 4)$ is:

$12b^2 - 28b + 16$

Let me know if you need any further explanations or have additional questions!

Here are 5 related questions for you to explore further:

1. How would you factor the expression $12b^2 - 28b + 16$?
2. What is the process for multiplying two binomials when one has a negative coefficient, like in this case?
3. How do you simplify expressions with two variables, like $(4x - 3)(2y + 5)$?
4. Can you identify the special product patterns (like difference of squares) and how they apply in different situations?
5. What are the steps to solve for $b$ in a quadratic equation, like $12b^2 - 28b + 16 = 0$?

Tip: When multiplying binomials, it's important to multiply each term in the first binomial by each term in the second. This ensures that no terms are skipped!