text: # Thread: factoring cubed function
  
  1. ## factoring cubed function
  
  (x+(DELTAX))^3
  
  i feel dumb but i totally forgot how to factor this so i can actually work with it in my calc class :O? any help
  
  2. Originally Posted by maybnxtseasn
  (x+(DELTAX))^3
  
  i feel dumb but i totally forgot how to factor this so i can actually work with it in my calc class :O? any help
  It is factored. Do you mean you want to multiply it?
  
  One way: $\displaystyle (x+\Delta x)^2= (x+ \Delta x)(x+ \Delta x)= x^2+ (\Delta x)(x)+ x(\Delta x)+ (\Delta x)^2$
  $\displaystyle = x^2+ 2x\Delta x+ (\Delta x)^2k$
  
  and then $\displaystyle (x+ \Delta x)^3= (x+ \Delta x)(x+ \Delta x)^2$$\displaystyle = (x+ \Delta x)(x^2+ 2x\Delta x+ (\Delta x)^2)$$\displaystyle = x(x^2)+ \Delta x(x^2)+ x(2x\Delta x)+ \Delta x(2x\Delta x)+ x(\Delta x)^2+ \Delta x(\Delta x)^2$
  $\displaystyle = x^2+ 3x^2\Delta x+ 3x(\Delta x)^2+ (\Delta x)^3$
  
  Quicker way: if you know the general formula $\displaystyle (a+ b)^3= a^3+ 3a^2b+ 3ab^2+ b^3$, use that with a= x and $\displaystyle b= \Delta x$ to get the same thing.
explanation: The document is a forum thread where a user asks for help in factoring a cubed function, specifically \((x + \Delta x)^3\). Another user responds by explaining that the expression is already factored and provides two methods to expand it: a step-by-step multiplication and using the binomial theorem. The thread contains a question and an answer.
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: # Thread: factoring cubed function
  
  1. ## factoring cubed function
  
  (x+(DELTAX))^3
  
  i feel dumb but i totally forgot how to factor this so i can actually work with it in my calc class :O? any help
  
  2. Originally Posted by maybnxtseasn
  (x+(DELTAX))^3
  
  i feel dumb but i totally forgot how to factor this so i can actually work with it in my calc class :O? any help
  It is factored. Do you mean you want to multiply it?
  
  One way: $\displaystyle (x+\Delta x)^2= (x+ \Delta x)(x+ \Delta x)= x^2+ (\Delta x)(x)+ x(\Delta x)+ (\Delta x)^2$
  $\displaystyle = x^2+ 2x\Delta x+ (\Delta x)^2k$
  
  and then $\displaystyle (x+ \Delta x)^3= (x+ \Delta x)(x+ \Delta x)^2$$\displaystyle = (x+ \Delta x)(x^2+ 2x\Delta x+ (\Delta x)^2)$$\displaystyle = x(x^2)+ \Delta x(x^2)+ x(2x\Delta x)+ \Delta x(2x\Delta x)+ x(\Delta x)^2+ \Delta x(\Delta x)^2$
  $\displaystyle = x^2+ 3x^2\Delta x+ 3x(\Delta x)^2+ (\Delta x)^3$
  
  Quicker way: if you know the general formula $\displaystyle (a+ b)^3= a^3+ 3a^2b+ 3ab^2+ b^3$, use that with a= x and $\displaystyle b= \Delta x$ to get the same thing.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a forum thread where a user asks for help in factoring a cubed function, specifically \((x + \Delta x)^3\). Another user responds by explaining that the expression is already factored and provides two methods to expand it: a step-by-step multiplication and using the binomial theorem. The thread contains a question and an answer.
  
  Label: question-and-answer