Binomial Theorem: Expansion, Examples, and Applications
Welcome to my Presentation
Hossain Md Waseem Firoz
Instructor (Mathematics)
Kushtia Polytechnic Institute
Chapter 3 (Binomial Theorem)
•
What Is Binomial Expansion In Math's?
Binomial expansion is to expand and write the
terms which are equal to the natural number
exponent of the sum or difference of two
terms. For two terms x and y the binomial
expansion to the power of n is (x + y)
n
=
n
C0 0
x
n
y
0
+
n
C1 1 x
n
-
1
y
1
+
n
C2 2 x
n-2
y
2
+
n
C3.
•
Binomial theorem
primarily helps to find the expanded value of the
algebraic expression of the form (x + y)
n
. Finding the value of (x +
y)
2
, (x + y)
3
, (a + b + c)
2
is easy and can be obtained by algebraically
multiplying the number of times based on the exponent value. But
finding the expanded form of (x + y)
17
or other such expressions
with higher exponential values involves too much calculation. It can
be made easier with the help of the binomial theorem.
•
The exponent value of this binomial theorem expansion can be a
negative number or a fraction. Here we limit our explanations to
only non-negative values. Let us learn more about the terms,
formula and the properties of coefficients in this binomial
expansion article.
•
•
The binomial theorem is also known as the
binomial expansion which gives the formula
for the expansion of the exponential power of
a
binomial expression
. Binomial expansion of
(x + y)
n
by using the binomial theorem is as
follows,
•
(x+y)
n
=
n
C
0
x
n
y
0
+
n
C
1
x
n-1
y
1
+
n
C
2
x
n-2
y
2
+ ...
+
n
C
n-1
x
1
y
n-1
+
n
C
n
x
0
y
n
Binomial theorem for Positive Index
Binomial theorem for Negative Index
Binomial theorem for Fractional Index
Examples of Binomial Expansion
Examples
Binomial theorem is a powerful mathematical concept used to expand expressions involving binomials. This presentation explores the basics of binomial expansion, formulae for positive, negative, and fractional indices, along with examples demonstrating its application. By leveraging the binomial theorem, complex algebraic expressions can be simplified efficiently, making calculations more manageable. Dive into the world of binomial theorem to unlock its potential in solving mathematical problems.
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Presentation Transcript
Welcome to my Presentation Hossain Md Waseem Firoz Instructor (Mathematics) Kushtia Polytechnic Institute
Chapter 3 (Binomial Theorem) What Is Binomial Expansion In Math's? Binomial expansion is to expand and write the terms which are equal to the natural number exponent of the sum or difference of two terms. For two terms x and y the binomial expansion to the power of n is (x + y)n=nC0 0 xny0+nC1 1 xn - 1y1+nC2 2 xn-2y2+nC3.
Binomial theorem primarily helps to find the expanded value of the algebraic expression of the form (x + y)n. Finding the value of (x + y)2, (x + y)3, (a + b + c)2is easy and can be obtained by algebraically multiplying the number of times based on the exponent value. But finding the expanded form of (x + y)17or other such expressions with higher exponential values involves too much calculation. It can be made easier with the help of the binomial theorem. The exponent value of this binomial theorem expansion can be a negative number or a fraction. Here we limit our explanations to only non-negative values. Let us learn more about the terms, formula and the properties of coefficients in this binomial expansion article.
The binomial theorem is also known as the binomial expansion which gives the formula for the expansion of the exponential power of a binomial expression. Binomial expansion of (x + y)nby using the binomial theorem is as follows, (x+y)n=nC0xny0+nC1xn-1y1+nC2xn-2y2+ ... +nCn-1x1yn-1+nCnx0yn
