The expression \((z + a)(z - b)\) can be expanded using the distributive property (also known as the FOIL method for binomials):

\[
(z + a)(z - b) = z(z - b) + a(z - b)
\]
\[
= z^2 - bz + az - ab
\]
\[
= z^2 + (a - b)z - ab
\]

So, the expanded form is:

\[
z^2 + (a - b)z - ab
\]

Would you like more details or have any other questions?

Here are 5 related questions for further practice:
1. What is the expansion of \((x + 3)(x - 4)\)?
2. How would you expand \((z + b)(z - b)\), which is a difference of squares?
3. Can you simplify the expression \((z + a)^2\)?
4. How do you factor \(z^2 - 5z + 6\)?
5. What happens if \(a = b\) in the expression \((z + a)(z - b)\)?

**Tip**: When expanding binomials, always distribute each term from the first binomial to each term in the second binomial.

Learn how to expand and simplify the expression (z + a)(z - b) using the distributive property, also known as the FOIL method for binomials. This solution covers key algebraic concepts such as polynomials and binomial expansion, suitable for students in Grades 8-10.

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