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Example Questions
Example Question #1 :How To Find The Value Of The Coefficient
What is the value of the coefficient in front of the term that includesin the expansion of?
Using the binomial theorem, the term containing thex2y7will be equal to
(2x)2(–y)7
=36(–4x2y7)= -144x2y7
Example Question #1 :Binomials
A function of the formpasses through the pointsand. What is the value of?
The easisest way to solve foris to begin by plugging each pair of coordinates into the function.
Using our first point, we will plug inforandfor. This gives us the equation
.
Squaring 0 gives us 0, and multiplying this bystill gives 0, leaving onlyon the right side, such that
.
We now know the value of, and we can use this to help us find. Substituting our second set of coordinates into the function, we get
which simplifies to
.
However, since we know, we can substitute to get
subtracting 7 from both sides gives
and dividing by 4 gives our answer
.
Example Question #3 :Binomials
is equivalent to which of the following?
To answer this problem, we need to multiply the expressions together, being mindful of how to correctly multiply like variables with exponents. To do this, we add the exponents together if the the like variables are being multiplied and subtract the exponents if the variables are being divided. So, for the presented data:
We then multiply the remaining expressions together. When we do this, we will multiply the coefficients together and combine the different variables into the final expression. Therefore:
This means our answer is.
Example Question #4 :Binomials
给coefficient ofin the product
.
While this problem can be answered by multiplying the three binomials, it is not necessary. There are three ways to multiply one term from each binomial such that twoterms and one constant are multiplied; find the three products and add them, as follows:
Add:.
The correct response is.
Example Question #1 :Binomials
给coefficient ofin the product
While this problem can be answered by multiplying the three binomials, it is not necessary. There are three ways to multiply one term from each binomial such that twoterms and one constant are multiplied; find the three products and add them, as follows:
Add:
The correct response is.
Example Question #1 :How To Find The Value Of The Coefficient
给coefficient ofin the binomial expansion of.
If the expressionis expanded, then by the binomial theorem, theterm is
or, equivalently, the coefficient ofis
Therefore, thecoefficient can be determined by setting
:
Example Question #2 :How To Find The Value Of The Coefficient
给coefficient ofin the binomial expansion of.
If the expressionis expanded, then by the binomial theorem, theterm is
or, equivalently, the coefficient ofis
Therefore, thecoefficient can be determined by setting
:
Example Question #1 :How To Find The Value Of The Coefficient
给coefficient ofin the binomial expansion of.
If the expressionis expanded, then by the binomial theorem, theterm is
or, equivalently, the coefficient ofis
Therefore, thecoefficient can be determined by setting
Example Question #9 :Binomials
给coefficient ofin the product
.
While this problem can be answered by multiplying the three binomials, it is not necessary. There are three ways to multiply one term from each binomial such that twoterms and one constant are multiplied; find the three products and add them, as follows:
Add:
The correct response is -122.
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