PSAT Math : Binomials

Study concepts, example questions & explanations for PSAT Math

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Example Questions

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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:

Explanation:

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:

Explanation:

Find the product:

Use the distributive property:

Write the resulting expression in standard form:

Example Question #382 : Algebra

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

 

 

Possible Answers:

20

16

18

22

Correct answer:

20

Explanation:

We first expand each binomial to get x2 + 2xy + y2 = 144  and x2 - 2xy + y2 = 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

Explanation:

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:

Explanation:

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:

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:

 

 

 

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:

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 .

Possible Answers:

Correct answer:

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 #5 : How To Find The Value Of The Coefficient

Give the coefficient of  in the binomial expansion of .

Possible Answers:

Correct answer:

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

.

Possible Answers:

Correct answer:

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:

 

 

 

Add: 

The correct response is -122.

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