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.