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.

Learn how to expand and simplify expressions like x^8z^4 - (a+3)^2. This solution explores polynomial and binomial operations, including expanding (a+3)^2 and simplifying terms. Suitable for students in Grades 10-12.

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