1. Stating the problem: Simplify the expression $$(x-1)^2 - 4x^2$$. 2. Use the formula for the square of a binomial: $$(a-b)^2 = a^2 - 2ab + b^2$$. 3. Expand $$(x-1)^2$$ using the formula: $$ (x-1)^2 = x^2 - 2x + 1 $$ 4. Substitute back into the expression: $$ x^2 - 2x + 1 - 4x^2 $$ 5. Combine like terms: $$ x^2 - 4x^2 - 2x + 1 = (1 - 4)x^2 - 2x + 1 = -3x^2 - 2x + 1 $$ 6. Final simplified expression is: $$ \boxed{-3x^2 - 2x + 1} $$