text: # Let a^6 - b^6 is simplified to (a - b) (a^2 - ab + b^2) k , then k is?
  
  ## Let ${a}^{6}$ - ${b}^{6}$ is simplified to (a - b) (${a}^{2}$ - ab + ${b}^{2}$) k, then k is?
  
  Mar 20, 2018
  
  The solution is $k = \left(a + b\right) \left({a}^{2} + a b + {b}^{2}\right)$.
  
  #### Explanation:
  
  ${a}^{6} - {b}^{6} = \left(a - b\right) \left({a}^{2} - a b + {b}^{2}\right) k$
  
  ${\left({a}^{3}\right)}^{2} - {\left({b}^{3}\right)}^{2} = \left(a - b\right) \left({a}^{2} - a b + {b}^{2}\right) k$
  
  Difference of squares factoring:
  
  $\left({a}^{3} - {b}^{3}\right) \left({a}^{3} + {b}^{3}\right) = \left(a - b\right) \left({a}^{2} - a b + {b}^{2}\right) k$
  
  Difference of cubes factoring:
  
  $\left(a - b\right) \left({a}^{2} + a b + {b}^{2}\right) \left({a}^{3} + {b}^{3}\right) = \left(a - b\right) \left({a}^{2} - a b + {b}^{2}\right) k$
  
  $\textcolor{red}{\cancel{\textcolor{b l a c k}{\left(a - b\right)}}} \left({a}^{2} + a b + {b}^{2}\right) \left({a}^{3} + {b}^{3}\right) = \textcolor{red}{\cancel{\textcolor{b l a c k}{\left(a - b\right)}}} \left({a}^{2} - a b + {b}^{2}\right) k$
  
  $\left({a}^{2} + a b + {b}^{2}\right) \left({a}^{3} + {b}^{3}\right) = \left({a}^{2} - a b + {b}^{2}\right) k$
  
  Sum of cubes factoring:
  
  $\left({a}^{2} + a b + {b}^{2}\right) \left(a + b\right) \left({a}^{2} - a b + {b}^{2}\right) = \left({a}^{2} - a b + {b}^{2}\right) k$
  
  $\left({a}^{2} + a b + {b}^{2}\right) \left(a + b\right) \textcolor{red}{\cancel{\textcolor{b l a c k}{\left({a}^{2} - a b + {b}^{2}\right)}}} = \textcolor{red}{\cancel{\textcolor{b l a c k}{\left({a}^{2} - a b + {b}^{2}\right)}}} k$
  
  $\left({a}^{2} + a b + {b}^{2}\right) \left(a + b\right) = k$
  
  $k = \left(a + b\right) \left({a}^{2} + a b + {b}^{2}\right)$
  
  That's the answer. Hope this helped!
explanation: The document contains a math question and a detailed step-by-step solution to the question. The question asks for the value of \( k \) in the given expression, and the solution provides the answer \( k = (a + b)(a^2 + ab + b^2) \).
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # Let a^6 - b^6 is simplified to (a - b) (a^2 - ab + b^2) k , then k is?
  
  ## Let ${a}^{6}$ - ${b}^{6}$ is simplified to (a - b) (${a}^{2}$ - ab + ${b}^{2}$) k, then k is?
  
  Mar 20, 2018
  
  The solution is $k = \left(a + b\right) \left({a}^{2} + a b + {b}^{2}\right)$.
  
  #### Explanation:
  
  ${a}^{6} - {b}^{6} = \left(a - b\right) \left({a}^{2} - a b + {b}^{2}\right) k$
  
  ${\left({a}^{3}\right)}^{2} - {\left({b}^{3}\right)}^{2} = \left(a - b\right) \left({a}^{2} - a b + {b}^{2}\right) k$
  
  Difference of squares factoring:
  
  $\left({a}^{3} - {b}^{3}\right) \left({a}^{3} + {b}^{3}\right) = \left(a - b\right) \left({a}^{2} - a b + {b}^{2}\right) k$
  
  Difference of cubes factoring:
  
  $\left(a - b\right) \left({a}^{2} + a b + {b}^{2}\right) \left({a}^{3} + {b}^{3}\right) = \left(a - b\right) \left({a}^{2} - a b + {b}^{2}\right) k$
  
  $\textcolor{red}{\cancel{\textcolor{b l a c k}{\left(a - b\right)}}} \left({a}^{2} + a b + {b}^{2}\right) \left({a}^{3} + {b}^{3}\right) = \textcolor{red}{\cancel{\textcolor{b l a c k}{\left(a - b\right)}}} \left({a}^{2} - a b + {b}^{2}\right) k$
  
  $\left({a}^{2} + a b + {b}^{2}\right) \left({a}^{3} + {b}^{3}\right) = \left({a}^{2} - a b + {b}^{2}\right) k$
  
  Sum of cubes factoring:
  
  $\left({a}^{2} + a b + {b}^{2}\right) \left(a + b\right) \left({a}^{2} - a b + {b}^{2}\right) = \left({a}^{2} - a b + {b}^{2}\right) k$
  
  $\left({a}^{2} + a b + {b}^{2}\right) \left(a + b\right) \textcolor{red}{\cancel{\textcolor{b l a c k}{\left({a}^{2} - a b + {b}^{2}\right)}}} = \textcolor{red}{\cancel{\textcolor{b l a c k}{\left({a}^{2} - a b + {b}^{2}\right)}}} k$
  
  $\left({a}^{2} + a b + {b}^{2}\right) \left(a + b\right) = k$
  
  $k = \left(a + b\right) \left({a}^{2} + a b + {b}^{2}\right)$
  
  That's the answer. Hope this helped!
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question and a detailed step-by-step solution to the question. The question asks for the value of \( k \) in the given expression, and the solution provides the answer \( k = (a + b)(a^2 + ab + b^2) \).
  
  Label: question-and-answer