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The given expression is:

\[
27m^2 - 36m + 12
\]

To factor this expression, we can first look for a common factor among all the terms.

1. The greatest common factor (GCF) of \(27m^2\), \(-36m\), and \(12\) is **3**. So, we can factor out 3 from the expression:

\[
27m^2 - 36m + 12 = 3(9m^2 - 12m + 4)
\]

2. Now, let's try to factor the quadratic expression \(9m^2 - 12m + 4\). We can use factoring by grouping or the quadratic formula, but this trinomial is a perfect square trinomial, meaning it factors as:

\[
9m^2 - 12m + 4 = (3m - 2)^2
\]

So the factored form of the expression is:

\[
3(3m - 2)^2
\]

Thus, the final factorization is:

\[
27m^2 - 36m + 12 = 3(3m - 2)^2
\]

Would you like more details or have any questions?

### Related Questions:
1. How do you factor out the greatest common factor (GCF)?
2. What is the process of factoring perfect square trinomials?
3. Can all quadratic expressions be factored into perfect squares?
4. How would you apply the quadratic formula to factor \(9m^2 - 12m + 4\)?
5. What are the different methods of factoring quadratic expressions?

### Tip:
When factoring, always check for a greatest common factor (GCF) first before attempting more complex methods like completing the square or using the quadratic formula.

Learn how to factor the quadratic expression 27m^2 - 36m + 12. This tutorial covers key algebraic concepts like factoring perfect square trinomials and using the greatest common factor (GCF). Suitable for students in Grades 9-11.

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