PSAT Math : How to simplify binomials

Study concepts, example questions & explanations for PSAT Math

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Example Questions

Example Question #22 : Polynomials

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

 

 

Possible Answers:

18

20

16

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.

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