1. **Problem statement:** Simplify and expand the expression $5(u+5)(u-5)(u+2)$. 2. **Recall the difference of squares formula:** $$(a+b)(a-b) = a^2 - b^2$$ This helps simplify $(u+5)(u-5)$. 3. **Apply the formula:** $$(u+5)(u-5) = u^2 - 25$$ 4. **Rewrite the original expression:** $$5(u^2 - 25)(u+2)$$ 5. **Expand $(u^2 - 25)(u+2)$ using distributive property:** $$u^2 \times u + u^2 \times 2 - 25 \times u - 25 \times 2 = u^3 + 2u^2 - 25u - 50$$ 6. **Multiply the entire expression by 5:** $$5(u^3 + 2u^2 - 25u - 50) = 5u^3 + 10u^2 - 125u - 250$$ **Final answer:** $$5u^3 + 10u^2 - 125u - 250$$