# ACT Math : How to find the value of the coefficient

## 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 includes in the expansion of ?

Explanation:

Using the binomial theorem, the term containing the x2 ywill be equal to

(2x)2(–y)7

=36(–4x2 y7)= -144x2y7

### Example Question #1 : Binomials

A function of the form  passes through the points  and .  What is the value of  ?

Explanation:

The easisest way to solve for  is to begin by plugging each pair of coordinates into the function.

Using our first point, we will plug in  for  and  for .  This gives us the equation

.

Squaring 0 gives us 0, and multiplying this by  still gives 0, leaving only  on 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 : How To Find The Value Of The Coefficient

is equivalent to which of the following?

Explanation:

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 #1 : How To Find The Value Of The Coefficient

Give the coefficient of  in the product

.

Explanation:

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 two  terms and one constant are multiplied; find the three products and add them, as follows:

The correct response is .

### Example Question #1 : How To Find The Value Of The Coefficient

Give the coefficient of  in the product

Explanation:

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 two  terms and one constant are multiplied; find the three products and add them, as follows:

The correct response is .

### Example Question #3 : How To Find The Value Of The Coefficient

Give the coefficient of  in the binomial expansion of .

Explanation:

If the expression  is expanded, then by the binomial theorem, the  term is

or, equivalently, the coefficient of  is

Therefore, the  coefficient can be determined by setting

:

### Example Question #1 : How To Find The Value Of The Coefficient

Give the coefficient of  in the binomial expansion of .

Explanation:

If the expression  is expanded, then by the binomial theorem, the  term is

or, equivalently, the coefficient of  is

Therefore, the  coefficient can be determined by setting

:

### Example Question #1 : How To Find The Value Of The Coefficient

Give the coefficient of  in the binomial expansion of .

Explanation:

If the expression  is expanded, then by the binomial theorem, the  term is

or, equivalently, the coefficient of  is

Therefore, the  coefficient can be determined by setting

### Example Question #6 : How To Find The Value Of The Coefficient

Give the coefficient of  in the product

.

Explanation:

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 two  terms and one constant are multiplied; find the three products and add them, as follows: