A binomial coefficient is a coefficient of any of the terms in the expansion of the binomial (x+y)^n.
Is the binomial expansion.
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.
The binomial expansion is valid for n less than 1.
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.