To factor the quadratic expression \( m^2 + 8m + 7 \), we look for two numbers that multiply to \( 7 \) (the constant term) and add up to \( 8 \) (the coefficient of the linear term).
The numbers \( 1 \) and \( 7 \) satisfy these conditions:
- \( 1 \times 7 = 7 \)
- \( 1 + 7 = 8 \)
Thus, we can factor the expression as:
\[ m^2 + 8m + 7 = (m + 1)(m + 7) \]
So, the factored form of the expression is \( (m + 1)(m + 7) \).