Find the factors of *m*2 - 10*m* + 25.

To factor the quadratic expression \( m^2 - 10m + 25 \), follow these steps:

1. **Identify the quadratic form**: The expression is in the standard quadratic form \( ax^2 + bx + c \), where \( a = 1 \), \( b = -10 \), and \( c = 25 \).

2. **Check if it can be factored as a perfect square**: A quadratic expression can be factored as a perfect square if it can be written in the form \( (m - k)^2 \).

3. **Find the square root of the first term**: The first term is \( m^2 \), and its square root is \( m \).

4. **Find the square root of the last term**: The last term is 25, and its square root is 5.

5. **Check the middle term**: The middle term should be \( 2 \times m \times 5 = 10m \). Since the middle term is \(-10m\), this confirms that the expression can be factored as:

\[
m^2 - 10m + 25 = (m - 5)(m - 5) = (m - 5)^2
\]

So, the factors of \( m^2 - 10m + 25 \) are \((m - 5)(m - 5)\) or simply \((m - 5)^2\).

Would you like further details or have any questions?

Here are 5 related questions:
1. How would you factor the quadratic expression \( m^2 + 10m + 25 \)?
2. What are the roots of the equation \( m^2 - 10m + 25 = 0 \)?
3. Can you factor the expression \( m^2 - 6m + 9 \) in a similar way?
4. How do you factor a quadratic expression that is not a perfect square?
5. How do you complete the square for the expression \( m^2 - 10m + 25 \)?

**Tip:** Always check if a quadratic expression is a perfect square by verifying if the middle term equals twice the product of the square roots of the first and last terms.

Learn how to factor the quadratic expression m^2 - 10m + 25 with a step-by-step solution. This problem covers key algebraic concepts, including factoring perfect square trinomials and the quadratic equation formula. Suitable for students in Grades 9-12.

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