g 2​ (x)=(x−1) 2 −(x+1) 2

Sure, let's simplify the function step by step:

g(x) = (x-1)² - (x+1)²

This is a difference of squares, which can be simplified using the formula a² - b² = (a - b)(a + b). Here, a = (x-1) and b = (x+1).

So,

g(x) = [(x-1) - (x+1)] * [(x-1) + (x+1)]

Simplify inside the brackets:

g(x) = [x - 1 - x - 1] * [x - 1 + x + 1]

g(x) = [-2] * [2x]

Finally,

g(x) = -4x

So, the simplified form of the function g(x) = (x-1)² - (x+1)² is g(x) = -4x.