### All PSAT Math Resources

## Example Questions

### Example Question #1 : How To Multiply Binomials With The Distributive Property

Decrease by 40%. Which of the following will this be equal to?

**Possible Answers:**

**Correct answer:**

A number decreased by 40% is equivalent to 100% of the number minus 40% of the number. This is taking 60% of the number, or, equivalently, multiplying it by 0.6.

Therefore, decreased by 40% is 0.6 times this, or

### Example Question #1 : How To Multiply Binomials With The Distributive Property

Find the product:

**Possible Answers:**

**Correct answer:**

Find the product:

Use the distributive property:

Write the resulting expression in standard form:

### Example Question #382 : Algebra

If 〖(x+y)〗^{2 }= 144 and 〖(x-y)〗^{2 }= 64, what is the value of xy?

**Possible Answers:**

20

16

18

22

**Correct answer:**

20

We first expand each binomial to get x^{2} + 2xy + y^{2} = 144 and x^{2} - 2xy + y^{2} = 64. We then subtract the second equation from the first to find 4xy = 80. Finally, we divide each side by 4 to find xy = 20.

### Example Question #1 : How To Simplify Binomials

Which of these expressions can be simplified further by collecting like terms?

**Possible Answers:**

None of the expressions in the other choices can be simplified further

**Correct answer:**

None of the expressions in the other choices can be simplified further

A binomial can be simplified further if and only if the two terms have the same combination of variables and the same exponents for each like variable. This is not the case in any of the four binomials given, so none of the expressions can be simplified further.

### Example Question #1 : How To Find The Solution Of A Rational Equation With A Binomial Denominator

Solve for .

**Possible Answers:**

**Correct answer:**

Factor the expression

numerator: find two numbers that add to 2 and multiply to -8 [use 4,-2]

denominator: find two numbers that add to 5 and multiply to -14 [use 7,-2]

new expression:

Cancel the and cross multiply.

### Example Question #2 : How To Find The Value Of The Coefficient

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 #1 : How To Find The Value Of The Coefficient

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 #1 : How To Find The Value Of The Coefficient

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 #5 : How To Find The Value Of The Coefficient

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 #6 : How To Find The Value Of The Coefficient

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.

Certified Tutor

Certified Tutor