1. **Stating the problem:** We need to expand and simplify the following expressions: a) $ (x - y)^2 $ b) $ (u - v)^2 $ c) $ (20 - 1)^2 $ d) $ (2a - 1)^2 $ 2. **Formula used:** The square of a binomial difference is given by the formula: $$ (A - B)^2 = A^2 - 2AB + B^2 $$ This means we square the first term, subtract twice the product of the two terms, and add the square of the second term. 3. **Step-by-step solutions:** a) For $ (x - y)^2 $: $$ (x - y)^2 = x^2 - 2xy + y^2 $$ b) For $ (u - v)^2 $: $$ (u - v)^2 = u^2 - 2uv + v^2 $$ c) For $ (20 - 1)^2 $: First calculate the difference: $$ 20 - 1 = 19 $$ Then square it: $$ 19^2 = 361 $$ Alternatively, using the formula: $$ (20 - 1)^2 = 20^2 - 2 \times 20 \times 1 + 1^2 = 400 - 40 + 1 = 361 $$ d) For $ (2a - 1)^2 $: $$ (2a - 1)^2 = (2a)^2 - 2 \times 2a \times 1 + 1^2 = 4a^2 - 4a + 1 $$ 4. **Final answers:** a) $ x^2 - 2xy + y^2 $ b) $ u^2 - 2uv + v^2 $ c) $ 361 $ d) $ 4a^2 - 4a + 1 $