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The given expression to multiply is:

\[
-8ab \left( x^2 + y^a - 4 \right)
\]

Now, distributing the \(-8ab\) term across the terms inside the parentheses:

1. \(-8ab \cdot x^2 = -8abx^2\)
2. \(-8ab \cdot y^a = -8aby^a\)
3. \(-8ab \cdot (-4) = 32ab\)

Putting all these together:

\[
-8abx^2 - 8aby^a + 32ab
\]

The final result is:

\[
-8abx^2 - 8aby^a + 32ab
\]

Would you like more details or explanations on any step?

Here are 5 related questions you might find interesting:
1. How can you distribute more complex terms?
2. What happens when we factor out common terms?
3. How does this method apply in polynomial multiplication?
4. What are some special cases in multiplication of binomials or trinomials?
5. Can you solve similar expressions with exponents that are fractions?

**Tip:** Always check for common factors after expanding terms to simplify the expression further.

Learn how to multiply polynomials using the distributive property. This example illustrates the multiplication of -8ab by the polynomial (x^2 + y^a - 4) to yield -8abx^2 - 8aby^a + 32ab. Suitable for students in Grades 8-10.

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