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- College algebra
- Sequences, probability, and
- Binomial theorem
Key equations
Binomial Theorem |
|
term of a binomial expansion |
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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
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What is the Binomial Theorem and what is its use?
The Binomial Theorem is defined as
and can be used to expand any binomial.
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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?
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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:
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Which expression cannot be expanded using the Binomial Theorem? Explain.
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-
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The expression
cannot be expanded using the Binomial Theorem because it cannot be rewritten as a binomial.
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Questions & Answers
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what is the features of gymnosperm
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how is urine formed in human
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malaria is caused by an insect called mosquito.
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Isaac
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Female anopheles mosquitoe is d carrier
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a canal is more needed in a root but a cavity is a bad effect
Commander
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respiration is the process in which we breath in oxygen and breath out carbon dioxide
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how are lungs work
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where does digestion begins
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stimulates the follicle to release the mature ovum into the oviduct
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what are the functions of Endocrine and pituitary gland
Chinaza
endocrine secrete hormone and regulate body process
Achor
while pituitary gland is an example of endocrine system and it's found in the Brain
Achor
Biology is the study of living organisms, divided into many specialized field that cover their morphology, physiology,anatomy, behaviour,origin and distribution.
Lisah
biology is the study of life.
Alfreda
Biology is the study of how living organisms live and survive in a specific environment
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Source:
OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
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