The expression you provided is:

$x^8z^4 - (a + 3)^2$

This can be interpreted as a subtraction between two terms:

1. The first term, $x^8z^4$, is a product of two powers, $x^8$ and $z^4$.
2. The second term, $(a + 3)^2$, is the square of the binomial $a + 3$.

To expand or simplify this, let's evaluate each term individually:

Expanded Form of Each Term

1. First Term:

   • $x^8z^4$ remains as it is because it’s already in simplified form.

2. Second Term:

   • Expanding $(a + 3)^2$ using the binomial formula: $(a + 3)^2 = a^2 + 6a + 9$

Thus, the expression can be rewritten as:

$x^8z^4 - a^2 - 6a - 9$

This is now a simplified, expanded form of the original expression.

Would you like further steps or details? Here are some related questions:

1. What if we replaced $a+3$ with another variable?
2. How would the expression change if we added a constant term to $x^8z^4$?
3. Can we factor this expanded expression further?
4. What if we substituted specific values for $x$, $z$, and $a$?
5. How would the expression differ if we used different exponents for $x$ and $z$?

Tip: Remember that expanding binomials like $(a + b)^2$ involves applying the distributive property twice.