query: Algebra. Multiplying binomials
positive_passages.docid: 126214
positive_passages.text: Multiplying Binomial Terms
negative_passages.docid: 25004
negative_passages.text: Proving $\binom{m}{n} + \binom{m}{n-1} = \binom{m+1}{n}$ algebraically
negative_passages.docid: 35342
negative_passages.text: Show that $ \sum_{n=2}^m \binom{n}{2} = \binom{m+1}{3}$
negative_passages.docid: 125220
negative_passages.text: Solving binomial theorem via induction
negative_passages.docid: 61270
negative_passages.text: Binomial Theorem Sum
negative_passages.docid: 69721
negative_passages.text: $(a,b) \mathbin\# (c,d)=(a+c,b+d)$ and $(a,b) \mathbin\&(c,d)=(ac-bd(r^2+s^2), ad+bc+2rbd)$. Multiplicative inverse?
negative_passages.docid: 146810
negative_passages.text: How to derive this binomial identity?
negative_passages.docid: 152084
negative_passages.text: Binomial-Theorem proof
negative_passages.docid: 15985
negative_passages.text: simplify $(a_1 + a_2 +a_3+... +a_n)^m$
negative_passages.docid: 154280
negative_passages.text: Show this equality (The factorial as an alternate sum with binomial coefficients).
negative_passages.docid: 41510
negative_passages.text: Multiplying and adding fractions
negative_passages.docid: 25744
negative_passages.text: Multiplication in Permutation Groups Written in Cyclic Notation
negative_passages.docid: 112374
negative_passages.text: Evaluate $ \binom{n}{0}+\binom{n}{2}+\binom{n}{4}+\cdots+\binom{n}{2k}+\cdots$
negative_passages.docid: 114277
negative_passages.text: Proving in Discrete Structures Problem that $2^N = \binom{N}{0} + \binom{N}{1} + \binom{N}{2} + \dots + \binom{N}{N}$
negative_passages.docid: 75367
negative_passages.text: Find a simple formula for $\binom{n}{0}\binom{n}{1}+\binom{n}{1}\binom{n}{2}+...+\binom{n}{n-1}\binom{n}{n}$
negative_passages.docid: 121279
negative_passages.text: Proving an Combination formula $ \binom{n}{k} = \binom{n-1}{k}+\binom{n-1}{k-1}$
negative_passages.docid: 112827
negative_passages.text: Find the sum of the binomial coefficients