How can 1+1=3 be possible? - Mathematics Stack Exchange So that's the "proof" The failure is at step 5, where you say that pq = pr p q = p r implies that q = r q = r; that's true only if you know p p is nonzero For instance 0 ⋅ 5 = 0 ⋅ 7 0 5 = 0 7, but that doesn't let you conclude that 5 = 7 5 = 7, because 0 0 has no multiplicative inverse In your case, the number b − a b a is playing the role of p p, and because b b and a a are the same
Binomial expansion of $ (1-x)^n$ - Mathematics Stack Exchange I'm not sure how appropriate it is to answer questions this old, but compared to the methods above, I feel the easiest way to see the answer to this question is to take a = -x And substitute that into the binomial expansion: (1+a)^n This yields exactly the ordinary expansion Then, by substituting -x for a, we see that the solution is simply the ordinary binomial expansion with alternating