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  # Polynomial Factorization - Series 2c
  
  FACTORING BINOMIALS USING DIFFERENCE OF TWO SQUARES
  
  Binomials of the general form m^2 - n^2 can be factored into terms
  
  (m - n)*(m + n).
  
  example5:
  9x^2 - 64 = (3x)^2 - (8)^2
  = (3x-8)*(3x+8)
  
  example6:
  4a^3 - 4a = 4a * (a^2 -1)
  = 4a * (a^2 - 1^2)
  = 4a * (a - 1)(a + 1)
  
  example7:
  x^4 - y^4 = (x^2)^2 - (y^2)^2
  = (x^2 - y^2) * (x^2 + y^2)
  = (x - y)*(x +y) *(x^2 +y^2)
  
  FACTORING BINOMIALS USING SUM AND DIFFERENCE OF TWO CUBES
  
  Binomials of the general form outlined below can be factored as described:
  
  a^3 + b^3 can be factored into (a + b) * (a^2 - ab + b^2)
  a^3 - b^3 can be factored into (a - b) * (a^2 + ab + b^2)
explanation: The document provides a detailed explanation of polynomial factorization, specifically focusing on factoring binomials using the difference of two squares and the sum and difference of two cubes. It includes several examples to illustrate the methods. The document does not contain a specific question or a question and answer.
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  # Polynomial Factorization - Series 2c
  
  FACTORING BINOMIALS USING DIFFERENCE OF TWO SQUARES
  
  Binomials of the general form m^2 - n^2 can be factored into terms
  
  (m - n)*(m + n).
  
  example5:
  9x^2 - 64 = (3x)^2 - (8)^2
  = (3x-8)*(3x+8)
  
  example6:
  4a^3 - 4a = 4a * (a^2 -1)
  = 4a * (a^2 - 1^2)
  = 4a * (a - 1)(a + 1)
  
  example7:
  x^4 - y^4 = (x^2)^2 - (y^2)^2
  = (x^2 - y^2) * (x^2 + y^2)
  = (x - y)*(x +y) *(x^2 +y^2)
  
  FACTORING BINOMIALS USING SUM AND DIFFERENCE OF TWO CUBES
  
  Binomials of the general form outlined below can be factored as described:
  
  a^3 + b^3 can be factored into (a + b) * (a^2 - ab + b^2)
  a^3 - b^3 can be factored into (a - b) * (a^2 + ab + b^2)
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document provides a detailed explanation of polynomial factorization, specifically focusing on factoring binomials using the difference of two squares and the sum and difference of two cubes. It includes several examples to illustrate the methods. The document does not contain a specific question or a question and answer.
  
  Label: no-question