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A binomial coefficient is a coefficient of any of the terms in the expansion of the binomial (x+y)^n.
Binomial Theorum
A binomial expansion is a mathematical expression that represents the expansion of a binomial raised to a positive integer power, typically expressed as ((a + b)^n). The expansion is given by the Binomial Theorem, which states that it can be expressed as a sum of terms in the form (\binom{n}{k} a^{n-k} b^k), where (\binom{n}{k}) is the binomial coefficient. Each term corresponds to different combinations of (a) and (b) multiplied by the coefficient, and the expansion includes all integer values of (k) from 0 to (n). This theorem is widely used in algebra, probability, and combinatorics.
The binomial theorem describes the algebraic expansion of powers of a binomial, hence it is referred to as binomial expansion.
The first two terms in a binomial expansion that aren't 0
A binomial coefficient is a coefficient of any of the terms in the expansion of the binomial (x+y)^n.
Binomial Theorum
Not true. The expansion will have one more term.
The coefficient of x^r in the binomial expansion of (ax + b)^n isnCr * a^r * b^(n-r)where nCr = n!/[r!*(n-r)!]
First i will explain the binomial expansion
The binomial theorem describes the algebraic expansion of powers of a binomial, hence it is referred to as binomial expansion.
Sounds pretty sexy, eh? See link. http://en.wikipedia.org/wiki/Binomial_expansion
The binomial expansion is valid for n less than 1.
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The first two terms in a binomial expansion that aren't 0
Binomial Expansion makes it easier to solve an equation. It brings an equation of something raised to a power down to a solveable equation without parentheses.
The binomial usually has an x2 term and an x term, so we complete the square by adding a constant term. If the coefficient of x2 is not 1, we divide the binomial by that coefficient first (we can multiply the trinomial by it later). Then we divide the coefficient of x by 2 and square that. That is the constant that we need to add to get the perfect square trinomial. Then just multiply that trinomial by the original coefficient of x2.