SAT Math : Binomials

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #14 : Polynomials

Define an operation  on the set of real numbers as follows:

For all real ,

How else could this operation be defined?

Possible Answers:

Correct answer:

Explanation:

, as the cube of a binomial, can be rewritten using the following pattern:

Applying the rules of exponents to simplify this:

Therefore, the correct choice is that, alternatively stated,

.

Example Question #1 : Binomials

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 #1 : How To Simplify Binomials

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

 

 

Possible Answers:

18

16

20

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.

 

 

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