### All PSAT Math Resources

## Example Questions

### Example Question #281 : Variables

Give the coefficient of in the product

**Possible Answers:**

**Correct answer:**

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:

Add:

The correct response is .

### Example Question #291 : Polynomials

Give the coefficient of in the binomial expansion of .

**Possible Answers:**

**Correct answer:**

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 #292 : Polynomials

Give the coefficient of in the binomial expansion of .

**Possible Answers:**

**Correct answer:**

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 #293 : Polynomials

Give the coefficient of in the binomial expansion of .

**Possible Answers:**

**Correct answer:**

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 #9 : Coefficients

Give the coefficient of in the product

.

**Possible Answers:**

**Correct answer:**

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:

Add:

The correct response is -122.

### Example Question #31 : Variables

Give the coefficient of in the product

.

**Possible Answers:**

**Correct answer:**

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:

Add: .

The correct response is .

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