1. **State the problem:** Factorize the expression $2m^2 + 4mn$. 2. **Recall the factoring rule:** To factor an expression, find the greatest common factor (GCF) of all terms and factor it out. 3. **Identify the GCF:** The terms are $2m^2$ and $4mn$. - The coefficients are 2 and 4; GCF is 2. - The variables are $m^2$ and $mn$; common variable factor is $m$. 4. **Write the GCF:** $2m$. 5. **Factor out the GCF:** $$2m^2 + 4mn = 2m(\cancel{m} + 2\cancel{n})$$ 6. **Simplify inside the parentheses:** $$2m(m + 2n)$$ 7. **Conclusion:** The factorized form is $2m(m + 2n)$. 8. **Match with options:** Option d is $2m(m + 2n)$, which is correct.