Table of Contents
Binomial Expressions
Binomial Theorem – Expansion: A binomial expression is an algebraic expression consisting of two terms, the first of which is a monomial and the second of which is a binomial. The monomial is always the first term, and the binomial is always the second term. The terms are separated by a plus sign or a minus sign.
- For example, the binomial expression 3x − 2 is written 3x − 2 = (3x) − (2) . The terms are 3x and −2, and the sign between them is a minus sign.
Binomial Expression
A binomial expression is an algebraic expression that can be written in the form of:
- ax + by
- where a and b are real numbers and x and y are variables.
Binomial Theorem Expansion
The Binomial theorem expansion is a mathematical formula that can be used to calculate the coefficients of a binomial expansion. The binomial theorem expansion is a series expansion of (x + y)n, where n is a positive integer. The coefficients in the expansion can be used to calculate the terms in the expansion.
Binomial Theorem Rules
The binomial theorem states that for any positive integer n, and any two positive integers a and b not both equal to 0,
- (a + b)n = an + bn
- This theorem can be proved using the methods of mathematical induction.
Applications of Binomial Theorem
- There are a number of real-world applications of the binomial theorem. One example is in the calculation of compound interest. In this application, the binomial theorem is used to calculate the interest earned on an initial investment over a given period of time. This interest is then compounded over the same period of time, and the resulting interest is calculated. This process is repeated until the desired number of periods have elapsed.
- Another application of the binomial theorem is in the calculation of probabilities. In this application, the binomial theorem is used to calculate the probability of a particular event occurring. This probability is then used to make decisions about whether or not to take a particular action.
