1. **State the problem:** Multiply the expression $(z-3)(z-3)$. 2. **Formula used:** This is a product of two identical binomials, which can be expanded using the identity for the square of a binomial: $$ (a - b)^2 = a^2 - 2ab + b^2 $$ 3. **Apply the formula:** Here, $a = z$ and $b = 3$. $$ (z - 3)^2 = z^2 - 2 \times z \times 3 + 3^2 $$ 4. **Calculate each term:** $$ z^2 - 6z + 9 $$ 5. **Final answer:** $$ (z-3)(z-3) = z^2 - 6z + 9 $$ This means when you multiply $(z-3)$ by itself, you get a quadratic expression with the terms $z^2$, $-6z$, and $9$.