1. **State the problem:** Expand and express the product $(2x+5)(x+10)$ as a trinomial. 2. **Formula used:** Use the distributive property (FOIL method) for binomials: $(a+b)(c+d) = ac + ad + bc + bd$. 3. **Apply the formula:** $$ (2x+5)(x+10) = 2x \cdot x + 2x \cdot 10 + 5 \cdot x + 5 \cdot 10 $$ 4. **Calculate each term:** $$ = 2x^2 + 20x + 5x + 50 $$ 5. **Combine like terms:** $$ = 2x^2 + \cancel{20x + 5x} + 50 $$ $$ = 2x^2 + 25x + 50 $$ 6. **Final answer:** The trinomial is $2x^2 + 25x + 50$.