Simplify $7a^3(3a^2 - a) - 8a(2a - 4)$.
To simplify this expression, I need to apply the distributive property and combine like terms. First, I distribute the $7a^3$ to each term inside the parentheses: $7a^3(3a^2 - a) = 21a^5 - 7a^4$. Then, I distribute the $-8a$ to each term inside the parentheses: $-8a(2a - 4) = -16a^2 + 32a$. Now I have $21a^5 - 7a^4 - 16a^2 + 32a$. To combine like terms, I need to look for terms that have the same degree of $a$, which means the same exponent of $a$. I see that there are no other terms with degree 5 or 4, so I can't combine those terms with anything else. There is also no term with degree 3, so I can skip that. For degree 2, I have $-16a^2$, which also has no other terms to combine with. For degree 1, I have $32a$, which also has no other terms to combine with. For degree 0, I have no constant term, so I can skip that. Therefore, there are no like terms to combine, and the expression is already in simplest form. 