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What is a binomial coefficient?
A binomial coefficient is a coefficient of any of the terms in the expansion of the binomial (x+y)^n.
What is The expansion of a binomial that involves a coefficient found by combinations?
Binomial Theorum
What is a bionomial expansion?
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.
What is a binominal theorem?
The binomial theorem describes the algebraic expansion of powers of a binomial, hence it is referred to as binomial expansion.
What is meant by the first two non-zero terms in an binomial expansion?
The first two terms in a binomial expansion that aren't 0
What is a binomial coefficient?
A binomial coefficient is a coefficient of any of the terms in the expansion of the binomial (x+y)^n.
What is The expansion of a binomial that involves a coefficient found by combinations?
Binomial Theorum
The expansion of a binomial that involves a coefficient found by combinations. The expansion will contain the same number of terms as the exponent of the original binomial. For each term the exponents?
Not true. The expansion will have one more term.
How do you find the coefficients of the terms in the binomial expansion?
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)!]
What is the relationship between the binomial expansion and binomial distribution?
First i will explain the binomial expansion
What is a binominal theorem?
The binomial theorem describes the algebraic expansion of powers of a binomial, hence it is referred to as binomial expansion.
What is binomial expansion?
Sounds pretty sexy, eh? See link. http://en.wikipedia.org/wiki/Binomial_expansion
Validity of binomial expansion for n less than 0?
The binomial expansion is valid for n less than 1.
What is the value of the binomial coefficient for 500 choose 100?
1000
What is meant by the first two non-zero terms in an binomial expansion?
The first two terms in a binomial expansion that aren't 0
What does an binomial expansion do?
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.
How do you complete the square to make a binomial a perfect-square trinomial?
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.
