1. **State the problem:** Simplify the expression $a^2 + 3a + 2 \times 5a^2 - 6a + 3$. 2. **Understand the expression:** The expression involves addition and multiplication. According to the order of operations, multiplication must be done before addition. 3. **Rewrite the expression clearly:** $$a^2 + 3a + (2 \times 5a^2) - 6a + 3$$ 4. **Calculate the multiplication:** $$2 \times 5a^2 = 10a^2$$ 5. **Substitute back:** $$a^2 + 3a + 10a^2 - 6a + 3$$ 6. **Combine like terms:** - Combine $a^2$ terms: $a^2 + 10a^2 = 11a^2$ - Combine $a$ terms: $3a - 6a = -3a$ - Constant term: $3$ 7. **Final simplified expression:** $$11a^2 - 3a + 3$$