text: # How do you combine (x^3 - x - 4) - (x^2 + x - 4)?
  
  Mar 5, 2018
  
  See a solution process below:
  
  #### Explanation:
  
  First, remove all of the terms from parenthesis. Be careful to handle the signs of each individual term correctly:
  
  ${x}^{3} - x - 4 - {x}^{2} - x + 4$
  
  Next, group like terms in descending order of the size of their exponents:
  
  ${x}^{3} - {x}^{2} - x - x - 4 + 4$
  
  Now, combine like terms:
  
  ${x}^{3} - {x}^{2} - 1 x - 1 x - 4 + 4$
  
  ${x}^{3} - {x}^{2} + \left(- 1 - 1\right) x + \left(- 4 + 4\right)$
  
  ${x}^{3} - {x}^{2} + \left(- 2\right) x + 0$
  
  ${x}^{3} - {x}^{2} - 2 x$
  
  Mar 5, 2018
  
  color(magenta)(=x(x+1)(x+2)
  
  #### Explanation:
  
  $\left({x}^{3} - x - 4\right) - \left({x}^{2} + x - 4\right)$
  
  Multiplying the bracket with the $-$ sign.
  
  $= {x}^{3} - x \cancel{- 4} - {x}^{2} - x \cancel{+ 4}$
  
  $= {x}^{3} - {x}^{2} - 2 x$
  
  $= x \left({x}^{2} - x - 2\right)$
  
  Identity$= {x}^{2} + \left(a + b\right) x + a b$ , where $x = x , a = 2$ & $b = - 1$
  
  $= x \left[x \left(x - 1\right) + 2 \left(x - 1\right)\right]$
  
  Taking the common bracket out:
  
  color(magenta)(=x(x+1)(x+2)
  
  ~Hope this helps! :)
explanation: The document contains a math question and a detailed answer to the question. The question asks how to combine the expressions \((x^3 - x - 4) - (x^2 + x - 4)\), and the answer provides a step-by-step solution to simplify the expression.
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: # How do you combine (x^3 - x - 4) - (x^2 + x - 4)?
  
  Mar 5, 2018
  
  See a solution process below:
  
  #### Explanation:
  
  First, remove all of the terms from parenthesis. Be careful to handle the signs of each individual term correctly:
  
  ${x}^{3} - x - 4 - {x}^{2} - x + 4$
  
  Next, group like terms in descending order of the size of their exponents:
  
  ${x}^{3} - {x}^{2} - x - x - 4 + 4$
  
  Now, combine like terms:
  
  ${x}^{3} - {x}^{2} - 1 x - 1 x - 4 + 4$
  
  ${x}^{3} - {x}^{2} + \left(- 1 - 1\right) x + \left(- 4 + 4\right)$
  
  ${x}^{3} - {x}^{2} + \left(- 2\right) x + 0$
  
  ${x}^{3} - {x}^{2} - 2 x$
  
  Mar 5, 2018
  
  color(magenta)(=x(x+1)(x+2)
  
  #### Explanation:
  
  $\left({x}^{3} - x - 4\right) - \left({x}^{2} + x - 4\right)$
  
  Multiplying the bracket with the $-$ sign.
  
  $= {x}^{3} - x \cancel{- 4} - {x}^{2} - x \cancel{+ 4}$
  
  $= {x}^{3} - {x}^{2} - 2 x$
  
  $= x \left({x}^{2} - x - 2\right)$
  
  Identity$= {x}^{2} + \left(a + b\right) x + a b$ , where $x = x , a = 2$ & $b = - 1$
  
  $= x \left[x \left(x - 1\right) + 2 \left(x - 1\right)\right]$
  
  Taking the common bracket out:
  
  color(magenta)(=x(x+1)(x+2)
  
  ~Hope this helps! :)
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question and a detailed answer to the question. The question asks how to combine the expressions \((x^3 - x - 4) - (x^2 + x - 4)\), and the answer provides a step-by-step solution to simplify the expression.
  
  Label: question-and-answer