### Instruction: Simplify $7a^3(3a^2 - a) - 8a(2a - 4)$.### Response: 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.