# Algebra 1 : How to find the value of the coefficient

## Example Questions

### 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 #2 : 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 #4 : 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 #41 : Variables

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 #3 : 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 -122.

### Example Question #4 : How To Find The Value Of The Coefficient

What is the value of the coefficient of ?

Explanation:

In order to determine the coefficient, we will need to fully simplify this expression.

The numerator of the first term shares an  variable, which can be divided.

Subtract this expression with .

The coefficient is the number in front of .  The coefficient is .