text: # 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.
explanation: The document contains two example questions related to simplifying binomials. The first example question includes a problem and its solution, while the second example question is a multiple-choice question with an explanation that no further simplification is possible.
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distilabel_metadata.role: system
distilabel_metadata.content: # 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.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains two example questions related to simplifying binomials. The first example question includes a problem and its solution, while the second example question is a multiple-choice question with an explanation that no further simplification is possible.
  
  Label: multiple-question-and-answer