Binomial Theorem – As the power will increase the expansion will become lengthy and tedious to calculate which is the main reason that people need to be clear about the basic technicalities associated with the binomial expression.
It is very much important for kids to be clear about the introduction of the concept of binomial theorem in mathematics because this is the best possible method of expanding any kind of expression that has been raised to any kind of finite power.
This is one of the most important tools for expansion and has a very good application in the world of algebra, probability and several other kinds of related fields as well. Binomial expression is the expression that will be containing two dissimilar terms for example A+ B, A cube plus B cube and several other kinds of related things.
The formula associated with the implementation of the binomial theorem has been explained as:
NCR = N factorial / N – R factorial into R factorial
Kids need to be clear about the proof of this particular theorem as well so that there is no problem at any point in time while dealing with and solving the questions. But apart from this they also need to be clear about the basic properties of the binomial expressions and the theorem. They have been explained as follows:
- The number of coefficients into the binomial expression will be equal to 2N + 1
- There will be N +1 terms in the expansion of X + Y raised to power N
- The first and the last terms will be X raised to power N and Y raised to power N respectively
- From the very beginning of the expansion, the powers of X will be decreasing from N up to 0 and the powers of A will be increasing from zero up to L.
- The general term of the expansion will be X + Y raised to power and then can be perfectly represented in the technical format.
- In the binomial expansion of X + Y raised to power NR TH term from the end will be N – R plus 2 TH term from the beginning.
Apart from all the above-mentioned points, it is also important for kids to be clear about the concept of Pascal‘s triangle so that there is no doubt at any point in time that everything will be perfectly implemented. This will be the best possible arrangement of the binomial coefficients into the triangular format and has been perfectly named after the French mathematician. The numbers in this particular pattern will be perfectly studied by the kids so that there will be no issue at any point in time and everything will be perfectly implemented in the whole process.
Some of the very basic terms of the binomial expansion have been explained as:
- The term which will help in symbolising all the terms of the binomial expansion will be the general term
- The total number of terms in the expansion will be equal to N + 1 and the middle term will always depend upon the value of N in the whole process.
- Identification of the particular term will be based upon simple steps so that there will be no issue at any point in time and people can implement the formulas very successfully.
- Numerically greatest term will be the term that would be based upon the implementation of any kind of formula in the whole process.
Apart from all the above-mentioned points people also need to be clear about the binomial expansion for the negative exponent so that they can solve the questions very easily without any kind of doubt. Hence, attending math online classes at Cuemath is very much advisable for kids to become masters of this particular topic.