The given expression is a quadratic expression: 

\[
m^2 - 20m + 100
\]

To simplify or factorize this, let's check if it can be factored.

### Step 1: Identify coefficients
The expression is in the form:

\[
am^2 + bm + c
\]

Here:
- \( a = 1 \)
- \( b = -20 \)
- \( c = 100 \)

### Step 2: Check for factorization
We can check if the quadratic is a perfect square by examining if:

\[
m^2 - 20m + 100 = (m - k)^2
\]

If we expand \( (m - k)^2 \), we get:

\[
(m - k)^2 = m^2 - 2km + k^2
\]

By comparing this with \( m^2 - 20m + 100 \), we can see that:
- \( 2k = 20 \Rightarrow k = 10 \)
- \( k^2 = 100 \)

Thus, the quadratic expression can be rewritten as:

\[
m^2 - 20m + 100 = (m - 10)^2
\]

### Final result:
\[
m^2 - 20m + 100 = (m - 10)^2
\]

This is a perfect square.

Would you like further details on this, or do you have any questions?

Here are 5 related questions you might find helpful:
1. What is the general form of a quadratic equation?
2. How can we complete the square to factorize a quadratic expression?
3. How do you solve quadratic equations using the quadratic formula?
4. What is the discriminant of a quadratic equation, and how is it useful?
5. How do perfect square trinomials relate to the vertex form of a quadratic function?

**Tip:** When a quadratic trinomial has the form \( ax^2 + bx + c \), checking if it's a perfect square can simplify the factoring process greatly.

Learn how to factor the quadratic expression m^2 - 20m + 100 by recognizing it as a perfect square trinomial. This detailed explanation covers the algebraic process, including key concepts like factorization and perfect squares. Suitable for students in Grades 8-10.

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