Let's solve the given expression by simplifying and combining similar terms.

The expression is:

$(3a^3 - 2a^2 - a - 1) - (3a^3 - 3a^2 + 2a + 1)$

Step-by-Step Simplification:

1. Distribute the negative sign through the second parentheses: $(3a^3 - 2a^2 - a - 1) - 3a^3 + 3a^2 - 2a - 1$

2. Combine like terms:

   • $3a^3 - 3a^3 = 0$
   • $-2a^2 + 3a^2 = a^2$
   • $-a - 2a = -3a$
   • $-1 - 1 = -2$

Thus, the simplified expression is:

$a^2 - 3a - 2$

Would you like more details or have any further questions?

Here are 5 related questions that might interest you:

1. What happens if the powers of $a$ were larger, say $a^5$, instead of $a^3$?
2. How would this change if there was an additional term, like $+5a$ in the expression?
3. Can you derive the same result by grouping terms before distributing the negative sign?
4. How can this type of expression be represented graphically?
5. What is the significance of finding and combining like terms?

Tip: Always distribute negative signs carefully, especially when subtracting entire expressions.