To factor the expression 2m^2 + 10m + 8, we first look for two numbers that multiply to the constant term (8) and add up to the coefficient of the middle term (10). In this case, those numbers are 2 and 4.
Then, we rewrite the middle term (10m) using these numbers:
2m^2 + 2m + 8m + 8
Next, we group the terms in pairs:
(2m^2 + 2m) + (8m + 8)
We factor out the common factors from each pair:
2m(m + 1) + 8(m + 1)
Now, we can see that both terms have a common factor of (m + 1):
(m + 1)(2m + 8)
Therefore, the factored form of the expression 2m^2 + 10m + 8 is (m + 1)(2m + 8).
