# PSAT Math : How to simplify binomials

## Example Questions

### Example Question #3 : Binomials

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

22

16

20

18

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?

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

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.
The text contains two example questions related to binomials, one of which has a question and an answer, and the other is a question about simplifying binomials with an answer stating that none of the given expressions can be simplified further.
multiple_questions_with_answers
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# PSAT Math : How to simplify binomials

## Example Questions

### Example Question #3 : Binomials

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

22

16

20

18

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?

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

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.
user
The text contains two example questions related to binomials, one of which has a question and an answer, and the other is a question about simplifying binomials with an answer stating that none of the given expressions can be simplified further.

TYPE: MULTIPLE_QUESTIONS_WITH_ANSWERS