# Importance of Binomial Theorem

I know Binomial Theorem is a quick way of expanding a Binomial Expression that has been raised to some power i.e ##(a+b)^n##. But why is it so important to expand ##(a+b)^n##. What is the practical use of this in Science and Engineering.

UltrafastPED
Gold Member
Here is some background:
http://ualr.edu/lasmoller/newton.html

Newton showed how to use fractional exponents; this leads to infinite series which converge if the exponent is between -1 and +1. In many cases the first few terms are used in approximations, especially if the expression is of the form (1+x)^n.

Here is some background:
http://ualr.edu/lasmoller/newton.html

Newton showed how to use fractional exponents; this leads to infinite series which converge if the exponent is between -1 and +1. In many cases the first few terms are used in approximations, especially if the expression is of the form (1+x)^n.

Hello UltrafastPED,
The link that you gave didn't answered my question. My question isn't whether ##(a+b)^n## is important or ##(1+x)^n##. My question is Why there is so much need to solve equations like ##(a+b)^n## or ##(1+x)^n##, So that we have devised Binomial Theorem to solve such equations. When in Engineering and Science we come across such equations.

SteamKing
Staff Emeritus
Homework Helper
Whenever we need to expand (a+b)$^{n}$, application of the binomial theorem means we don't have to multiply a bunch of binomial expressions together. Kids nowadays take for granted having a symbolic algebra program like Mathematica or Maple, but in the olden days, the B.T. could save a lot of time doing algebra (and be more accurate to boot, avoiding a lot of mistakes which might otherwise go undetected). The binomial coefficients are also the same as the entries in Pascal's triangle, and there is a simple algorithm which allows one to calculate these entries by using the first two rows of the triangle.

http://en.wikipedia.org/wiki/Pascal's_triangle

Whenever we need to expand (a+b)$^{n}$, application of the binomial theorem means we don't have to multiply a bunch of binomial expressions together. Kids nowadays take for granted having a symbolic algebra program like Mathematica or Maple, but in the olden days, the B.T. could save a lot of time doing algebra (and be more accurate to boot, avoiding a lot of mistakes which might otherwise go undetected). The binomial coefficients are also the same as the entries in Pascal's triangle, and there is a simple algorithm which allows one to calculate these entries by using the first two rows of the triangle.

http://en.wikipedia.org/wiki/Pascal's_triangle

You didn't understand my question. Please read my above comment on "UltrafastPED"

SteamKing
Staff Emeritus