Originally Posted by

**exp13** Has left me so very confused:

Un+1= 5^n+1+(-8)^n+1

Un-1= 5^n-1+(-8)^n-1

Un^2 =5^2n+2(5^n(-8)^n)+(-8)^2n

Un+1Un-1 = 5^2n+5^n+1(-8)^n-1+5^n-1(-8)^n+1+(-8)^2n

after cancelling

Un+1Un-1-Un^2 = 5^2n + 5^n+1(-8)^n-1 + + 5^n-1(-8)^n+1 +(-8)^2n - (5^2n + 2(5^n(-8)^n) + (-8)^2n

= 5^n+1(-8)^n-1 + 5^n-1(-8)^n+1 - 2(5^n(-8)^n)

= 5^n-1(-8)^n-1 * (5^2+(-8)^2 - (2*5*(-8))

= (-40)^n-1 * (89-(-80))

= 169(-40)^n-1

If someone could please explain how the simplifications/cancellations (shown in red, previous steps are fine) have occurred, it would be much appreciated!