using binomial theorem prove that (x^n-y^n) is divisible by (x-y) - Maths - Binomial Theorem

Question

using binomial theorem prove that (x^n-y^n) is divisible by (x-y)

Manbar Singh · Accepted Answer

xn = x-y+yn⇒xn = x-y+yn⇒xn = x-yn+C1nx-yn-1
y +C2nx-yn-2 y2 +  +Cn-1nx-y yn-1 +Cnn
yn⇒xn = x-yn+C1nx-yn-1 y +C2nx-yn-2
y2 +  +Cn-1nx-y
yn-1 +yn⇒xn-yn = x-yn+C1nx-yn-1
y +C2nx-yn-2 y2 +  +Cn-1nx-y
yn-1 ⇒xn-yn =x-yx-yn-1+nyx-yn-2 + 
+Cn-1nyn-1So, xn-yn is clearly divisible by x-y