The given expression is:

\[
(6m - 6)^2
\]

This is a binomial square, which can be expanded using the formula:

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

Here, \( a = 6m \) and \( b = 6 \). Applying the formula:

\[
(6m - 6)^2 = (6m)^2 - 2(6m)(6) + (6)^2
\]

Now, let's simplify step by step:

\[
(6m)^2 = 36m^2
\]
\[
-2(6m)(6) = -72m
\]
\[
(6)^2 = 36
\]

Thus, the expanded form is:

\[
36m^2 - 72m + 36
\]

If you have any questions or would like further details, feel free to ask!

Here are some related questions:
1. How do you factor a quadratic expression?
2. What is the difference between binomial expansion and factoring?
3. Can you solve for \( m \) if the expression is set equal to zero?
4. How do you apply the quadratic formula to solve quadratic equations?
5. What is the importance of completing the square in solving quadratic equations?

**Tip:** When expanding binomials, always apply the square formula carefully to avoid missing terms.

Explore how to expand the binomial expression (6m - 6)^2 using algebraic principles. This step-by-step guide covers the binomial square formula and simplifies the expression to 36m^2 - 72m + 36. Perfect for students in Grades 8-10.

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