1. **State the problem:** Add the polynomials $$-10a^2 + 6a^3 + 3a$$ and $$-6a^3 - 4a + 8a^2$$. 2. **Write the polynomials together:** $$(-10a^2 + 6a^3 + 3a) + (-6a^3 - 4a + 8a^2)$$ 3. **Group like terms:** $$6a^3 + (-6a^3) + (-10a^2 + 8a^2) + (3a - 4a)$$ 4. **Add the coefficients of like terms:** - For $a^3$: $$6a^3 - 6a^3 = \cancel{6a^3} - \cancel{6a^3} = 0$$ - For $a^2$: $$-10a^2 + 8a^2 = -2a^2$$ - For $a$: $$3a - 4a = -1a = -a$$ 5. **Write the simplified sum:** $$-2a^2 - a$$ **Final answer:** $$-2a^2 - a$$