To simplify the given expression \( m^2 - 12m + 35 \), we can factorize it into two binomials.

### Step 1: Identify the factors of the quadratic expression

The expression is in the form of \( m^2 - 12m + 35 \), which matches the standard form of a quadratic equation \( ax^2 + bx + c \). Here:

- \( a = 1 \) (coefficient of \( m^2 \))
- \( b = -12 \) (coefficient of \( m \))
- \( c = 35 \) (constant term)

### Step 2: Find factors of 35 that add up to -12

We need to find two numbers that multiply to \( 35 \) (the constant term) and add up to \( -12 \) (the middle term coefficient).

The factors of 35 that work are \(-7\) and \(-5\):

\[
-7 \times -5 = 35 \quad \text{and} \quad -7 + (-5) = -12
\]

### Step 3: Factorize the expression

Using these factors, we can rewrite the quadratic expression:

\[
m^2 - 12m + 35 = (m - 7)(m - 5)
\]

### Final Factored Form

\[
m^2 - 12m + 35 = (m - 7)(m - 5)
\]

Would you like further details or have any questions?

### Related Questions

1. How would you factorize \( m^2 - 14m + 49 \)?
2. What is the general method to factorize any quadratic expression?
3. Can you solve the equation \( m^2 - 12m + 35 = 0 \)?
4. How do you complete the square for \( m^2 - 12m + 35 \)?
5. What are the solutions for \( (m - 7)(m - 5) = 0 \)?

### Tip

When factoring quadratics, always look for pairs of factors of the constant term that sum to the coefficient of the linear term.

Discover how to factor the quadratic expression m^2 - 12m + 35 into (m - 7)(m - 5) using simple algebraic techniques. This solution is ideal for students in Grades 8-10 and covers essential concepts in algebra, including the quadratic equation and factorization.

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