1. The problem is to expand and simplify the perfect square polynomial $ (c - 2)^2 $. 2. Recall the formula for the square of a binomial: $$ (a - b)^2 = a^2 - 2ab + b^2 $$ 3. Here, $a = c$ and $b = 2$. Substitute these into the formula: $$ (c - 2)^2 = c^2 - 2 \times c \times 2 + 2^2 $$ 4. Simplify the middle term and the last term: $$ c^2 - \cancel{2} \times c \times \cancel{2} + 4 = c^2 - 4c + 4 $$ 5. Therefore, the expanded and simplified form is: $$ c^2 - 4c + 4 $$ 6. Filling in the blanks in the original expression: $$ (c - 2)^2 = c^2 - 4c + 4 $$