The expression \((3k - 4)(3k - 4)\) is a product of two identical binomials, which is a perfect square trinomial. To expand this, we can apply the formula for the square of a binomial: 

\[
(a - b)^2 = a^2 - 2ab + b^2
\]

Here, \(a = 3k\) and \(b = 4\). 

So,

\[
(3k - 4)(3k - 4) = (3k)^2 - 2(3k)(4) + 4^2
\]

Now, let's calculate each term:

- \((3k)^2 = 9k^2\)
- \(2(3k)(4) = 24k\)
- \(4^2 = 16\)

Putting it all together:

\[
(3k - 4)(3k - 4) = 9k^2 - 24k + 16
\]

So, the expanded form is:

\[
9k^2 - 24k + 16
\]

Would you like any further explanation or details on this? 

Here are five related questions you might find interesting:

1. How would you expand \((2k + 5)(2k + 5)\)?
2. What happens if the binomials are different, like \((3k - 4)(3k + 4)\)?
3. Can you factorize the expression \(9k^2 - 24k + 16\) back into binomials?
4. How do you handle expressions like \((3k - 4)(3k + 2)\)?
5. What is the general formula for the square of any binomial \((a \pm b)^2\)?

**Tip:** When working with polynomials, always keep in mind common identities like the square of a binomial, as they can greatly simplify the expansion process.

Learn how to expand and simplify the expression (3k - 4)(3k - 4) step-by-step. This problem involves the square of a binomial formula and perfect square trinomials, crucial in algebraic manipulations. Suitable for Grades 9-12 students.

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