-
-
-
-
Key equations
Binomial Theorem |
|
term of a binomial expansion |
|
Key concepts
-
is called a binomial coefficient and is equal to
See
[link] .
- The Binomial Theorem allows us to expand binomials without multiplying. See
[link] .
- We can find a given term of a binomial expansion without fully expanding the binomial. See
[link] .
Section exercises
Verbal
What is a binomial coefficient, and how it is calculated?
A binomial coefficient is an alternative way of denoting the combination
It is defined as
Got questions? Get instant answers now!
What is the Binomial Theorem and what is its use?
The Binomial Theorem is defined as
and can be used to expand any binomial.
Got questions? Get instant answers now!
Algebraic
For the following exercises, evaluate the binomial coefficient.
For the following exercises, use the Binomial Theorem to expand each binomial.
For the following exercises, use the Binomial Theorem to write the first three terms of each binomial.
For the following exercises, find the indicated term of each binomial without fully expanding the binomial.
Graphical
For the following exercises, use the Binomial Theorem to expand the binomial
Then find and graph each indicated sum on one set of axes.
Extensions
In the expansion of
each term has the form
successively takes on the value
If
what is the corresponding term?
Got questions? Get instant answers now!
Find
and write the answer as a binomial coefficient in the form
Prove it.
Hint: Use the fact that, for any integer
such that
Proof:
Got questions? Get instant answers now!
Which expression cannot be expanded using the Binomial Theorem? Explain.
-
-
-
-
The expression
cannot be expanded using the Binomial Theorem because it cannot be rewritten as a binomial.
Got questions? Get instant answers now!
Questions & Answers
By the definition, is such that 0!=1.why?
(1+cosA+IsinA)(1+cosB+isinB)/(cos@+isin@)(cos$+isin$)
how we can draw three triangles of distinctly different shapes. All the angles will be cutt off each triangle and placed side by side with vertices touching
bsc F. y algebra and trigonometry pepper 2
given that x= 3/5 find sin 3x
remove any signs and collect terms of -2(8a-3b-c)
is that a real answer
Joeval
x²-2x+9-4x²+12x-20
-3x²+10x+11
Miranda
x²-2x+9-4x²+12x-20
-3x²+10x+11
Miranda
(X2-2X+8)-4(X2-3X+5)=0 ?
master
The anwser is imaginary
number if you want to know The anwser of the expression
you must arrange The expression and use quadratic formula To find the
answer
master
The anwser is imaginary
number if you want to know The anwser of the expression
you must arrange The expression and use quadratic formula To find the
answer
master
X2-2X+8-4X2+12X-20=0
(X2-4X2)+(-2X+12X)+(-20+8)= 0
-3X2+10X-12=0
3X2-10X+12=0
Use quadratic formula To find the answer
answer (5±Root11i)/3
master
Soo sorry (5±Root11* i)/3
master
x2-2x+8-4x2+12x-20
x2-4x2-2x+12x+8-20
-3x2+10x-12
now you can find the answer using quadratic
Mukhtar
explain and give four example of hyperbolic function
What is the correct rational algebraic expression of the given "a fraction whose denominator is 10 more than the numerator y?
Find nth derivative of eax sin (bx + c).
Find area common to the parabola y2 = 4ax and
x2 = 4ay.
Anurag
y2=4ax= y=4ax/2. y=2ax
akash
A rectangular garden is 25ft wide. if its area is 1125ft, what is the length of the garden
to find the length I divide the area by the wide wich means 1125ft/25ft=45
Miranda
What do you call a relation where each element in the domain is related to only one value in the range by some rules?
given 4cot thither +3=0and 0°<thither <180°
use a sketch to determine the value of the following
a)cos thither
nothing up todat yet
Miranda
aap konsi country se ho
jai
which language is that
Miranda
what is the formula for calculating algebraic
I think the formula for calculating algebraic is the statement of the equality of two expression stimulate by a set of addition, multiplication, soustraction, division, raising to a power and extraction of Root. U believe by having those in the equation you will be in measure to calculate it
Miranda
Source:
OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
Google Play and the Google Play logo are trademarks of Google Inc.