The value of a 2×2 determinant acbd is given by ad−bc.
Δ=x2−x+1x+1x−1x+1
Multiply the diagonal elements:
\Delta = (x^2 - x + 1)(x + 1) - (x - 1)(x + 1)$ We use two standard algebraic identities: 1. Sum of cubes: $(x+1)(x^2 - x + 1) = x^3 + 1^3$ 2. Difference of squares: $(x-1)(x+1) = x^2 - 1^2$ Substitute these back into the expression:\Delta = (x^3 + 1) - (x^2 - 1)\Delta = x^3 + 1 - x^2 + 1\Delta = x^3 - x^2 + 2$$