A Nice Algebra Problem | Simplify Without Calculators! 

謝謝，訓練腦力。

2^51-2^26+1

All I can I say about this, this is just BEAUTIFUL!!!

1+2^51-2^ 26

Let 2^25 = t, the given becomes E = N/D where N = 1 +16t^4 -4t^4 -8t^4 = 1 + 4t^4, D = 1 + 2t + 2t^2. Then, further manipulating N N = 1 +4t^4 = 1 +(2t^2)^2 = (1 +2t^2)^2 - 4t^2 N = (1 +2t^2)^2 - (2t)^2 =(1 +2t^2 -2t)(1 +2t^2 +2t) Thus, E = N/D = (1 +2t^2 -2t) = 1 +(2^25)^2 -2(2^25) = 1 +2^50 -2^26 E = 1 + 4^25 -4^13

(x ➖ 2x+1)

That is not algebra