Question

Simplify: ((2x^n)^2 - 1)/(2x^n-1)

where x is an integer and n is a positive interger.

Answer 1

a^2-b^2 = (a+b)(a-b)

(2x^n)^2 - 1 = (2x^n - 1)(2x^n + 1)
so, dividing by (2x^n-1) leaves you with just

2x^n + 1