In mathematics, you might have heard about various theorems such as – Pythagoras theorem, Ceva’s theorem, Bayes theorem, remainder theorem, and so on. Likewise, binomial theorem is a type of theorem which is basically used to find the value of an algebraic expression which is in the form of ‘(a+b)n where ‘n’ is defined as the integers and a and b are the variables. The binomial theorem is also used in order to find the value of larger exponential values. The resultant value can be a number or a fraction that is negative in nature. One of the famous mathematicians who was known by the name of Euclids started with this term around 4 BC (Before Christ). In this article, we will try to cover some basic concepts regarding binomial theorem such as significant terms, pascals triangle trend, and a detailed analysis.
A series of binomial coefficients which is carried out in a triangular form is defined as the pascal’s triangle. This term was given out by the name of a famous physicist and mathematician, Blaise Pascal. The values which we get from the coefficient of binomial theorem have a special trend which is generally observed in the pascal triangle. In this triangle, the borders or the outline of the triangle have the elements as the number 1, and others are managed in such an arrangement that each number will be the sum of the other two numbers which is placed just above them. The combination formula is used in order to give the value for the expansion of binomial coefficients.
Important Points Related to Binomial Theorem
As mentioned above, binomial theorem is a type of theorem which is used to find the values expanded in the algebraic expression. In this paragraph, we will try to cover some important points related to the theorem. The following points below analyze the terms related to it.
- The resultant or expanded value that we get will always be a negative fraction or a negative real number.
- Each and every term which is associated with the binomial theorem has a relation with the value which is numeric. This numeric value is also regarded as the coefficient.
- The binomial theorem is used to find the larger or expanded forms of values which cannot be calculated by the help of algebra. Thus, expressions with larger exponential values can only be calculated with binomial theorem.
- In the formula of binomial theorem, you will observe that there is a presence of variables and integers. Thus, the sum of two variables namely a and b will always be n which is an integer. If you want to learn about binomial theorems in a detailed manner, a fun way, and an interactive manner, you may visit Cuemath.
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