Pregunta
The term
is a term in which binomial
expansion?
expansion?
Ask by Cross Morgan. in the United States
Nov 09,2024
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The term
does not appear in either of the given binomial expansions.
Solución
To determine in which binomial expansion the term
appears, we will analyze both expressions given.
-
For the first expression:We can start by expanding both the numerator and the denominator.
-
The numerator
can be expanded using the binomial theorem: -
The denominator
can also be expanded:
To find the term, we need to consider the combined effect of both expansions. The termin corresponds to : where. The termin the denominator corresponds to : where, , and . Thus, the coefficient ofin the denominator is: The overall coefficient ofin the entire expression is: Since we are looking for the term, we can see that this term does not appear in this expression. -
-
For the second expression:The term
cannot appear in since it only contains the terms and .
In conclusion, the term
does not appear in either of the given binomial expansions.
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Como
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Bonus Knowledge
The term
appears in the binomial expansion of
. In the expansion, the general term can be expressed as
. For
, setting
(which gives
), we find the coefficient
which equals 35, yielding the exact term
.
Meanwhile, consider how this ties into the real-world! The binomial expansion isn’t just abstract math—engineers and scientists use it everyday in physics for calculating probabilities, distributions, and even optimizing designs based on varying parameters. So the next time you expand a binomial, remember it’s not just a number crunch; it’s real-world problem-solving at its best!

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