BINOMIAL THEOREM Meaning and
Definition
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The binomial theorem is a fundamental concept in algebra and mathematical analysis that expresses the expansion of a binomial raised to a positive integer power. It states that for any real numbers a and b, and a positive integer n, the expression (a+b)^n can be expanded as a sum of terms. These terms are determined by the coefficients of the expansion, which follow a specific pattern.
More precisely, the binomial theorem states that the expression (a+b)^n can be written as the sum from k=0 to n of the binomial coefficients, also known as the combination coefficients or Pascal's triangle coefficients, multiplied by a raised to the power of n-k, multiplied by b raised to the power of k. These binomial coefficients are derived from the combinatorial concept of choosing k objects out of n.
The binomial theorem provides a concise way to expand and simplify expressions involving binomials raised to powers, without the need for tedious and time-consuming multiplication. It is a powerful tool used in various areas of mathematics and physics, such as in probability theory, calculus, and algebraic equations. The theorem allows for efficient calculations and helps in analyzing and understanding the behavior of polynomial functions.
Common Misspellings for BINOMIAL THEOREM
- vinomial theorem
- ninomial theorem
- hinomial theorem
- ginomial theorem
- bunomial theorem
- bjnomial theorem
- bknomial theorem
- bonomial theorem
- b9nomial theorem
- b8nomial theorem
- bibomial theorem
- bimomial theorem
- bijomial theorem
- bihomial theorem
- binimial theorem
- binkmial theorem
- binlmial theorem
- binpmial theorem
- bin0mial theorem
Etymology of BINOMIAL THEOREM
The word "binomial" is derived from the Latin word "binomius", which consists of the root words "bi-" meaning "two" and "-nomius" meaning "name" or "term". The term "theorem" comes from the ancient Greek word "theorema", which means "a spectator's view" or "a proposition to be proved". Therefore, the etymology of the phrase "binomial theorem" suggests that it refers to a proposition or formula that pertains to the terms or names involving two variables or expressions.
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