1. **State the problem:** We need to find which expression is equivalent to $38(251m - 45)$. 2. **Use the distributive property:** The distributive property states that $a(b - c) = ab - ac$. Here, $a=38$, $b=251m$, and $c=45$. 3. **Apply the distributive property:** $$38(251m - 45) = 38 \times 251m - 38 \times 45$$ 4. **Calculate each term:** $$38 \times 251m = 9538m$$ $$38 \times 45 = 1710$$ 5. **Write the equivalent expression:** $$9538m - 1710$$ 6. **Compare with given options:** - Option F: $38 \cdot 251m - 38 \cdot 45$ matches the distributive property exactly. - Option G: $38(206m)$ is incorrect because $206m$ is not the result of $251m - 45$. - Option H: $-7(251m)$ is incorrect because the factor is not $-7$. - Option J: $38 \cdot 251m - 45$ is incorrect because $45$ is not multiplied by $38$. **Final answer:** Option F is equivalent to $38(251m - 45)$.