Which of the following expressions is a polynomial identity for all n≥1n \geq 1n≥1?
xn−1=(x−1)(xn−1+xn−2+⋯+x+1)x^n - 1 = (x - 1)(x^{n-1} + x^{n-2} + \cdots + x + 1)xn−1=(x−1)(xn−1+xn−2+⋯+x+1)
xn+1=(x+1)(xn−1−xn−2+⋯+1)x^n + 1 = (x + 1)(x^{n-1} - x^{n-2} + \cdots + 1)xn+1=(x+1)(xn−1−xn−2+⋯+1) for all nnn
xn−1=(x−1)nx^n - 1 = (x - 1)^nxn−1=(x−1)n
xn+1=(x+1)nx^n + 1 = (x + 1)^nxn+1=(x+1)n