text: Maharashtra State BoardSSC (English Medium) 7th Standard
  
  # Expansion of (a - b)2 = a2 - 2ab + b2
  
  ## Formula
  
  (a - b)2 = a2 - 2ab + b2.
  
  ## Notes
  
  ### Expansion of (a - b)2 = a2 - 2ab + b2:
  
  In the above figure, the square with side a is divided into 4 rectangles,
  namely, square with side (a - b), square with side b, and two rectangles of
  sides (a - b) and b.
  
  A (square I) + A (rectangle II) + A (rectangle III) + A (square IV) = A (□ PQRS)
  
  (a - b)2 + (a - b)b + (a - b)b + b2 = a2
  
  (a - b)2 + 2ab - 2b2 + b2 = a2
  
  (a - b)2 + 2ab - b= a2
  
  ∴ (a - b)2 = a2 - 2ab + b2
  
  Let us multiply the algebraic expressions and obtain the formula.
  (a - b)2 = (a - b) × (a - b)
  (a - b)2 = a (a - b) - b (a - b)
  (a - b)2 = a2 - ab - ab + b2
  (a - b)2 = a2 - 2ab + b2.
  
  ## Example
  
  Expand: (5x - 4)2
  
  (5x - 4)2
  
  = (5x)2 - 2(5x) x (4) + 42
  
  = 25x2 - 40x + 16.
  
  ## Example
  
  Expand: (98)2
  
  (98)2
  
  = (100 - 2)2
  
  = 1002 - 2 x 100 x 2 + 22
  
  = 10000 - 400 + 4
  
  = 9604.
  
  If you would like to contribute notes or other learning material, please submit them using the button below.
  
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explanation: The document is a section from a mathematics textbook or educational material, specifically for the 7th Standard of the Maharashtra State Board. It covers the expansion of the algebraic expression \((a - b)^2\). The document includes the formula, a detailed derivation, and two examples of how to apply the formula to expand specific expressions. The document does not contain a question or an answer in the form of a query or exercise.
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distilabel_metadata.content: Maharashtra State BoardSSC (English Medium) 7th Standard
  
  # Expansion of (a - b)2 = a2 - 2ab + b2
  
  ## Formula
  
  (a - b)2 = a2 - 2ab + b2.
  
  ## Notes
  
  ### Expansion of (a - b)2 = a2 - 2ab + b2:
  
  In the above figure, the square with side a is divided into 4 rectangles,
  namely, square with side (a - b), square with side b, and two rectangles of
  sides (a - b) and b.
  
  A (square I) + A (rectangle II) + A (rectangle III) + A (square IV) = A (□ PQRS)
  
  (a - b)2 + (a - b)b + (a - b)b + b2 = a2
  
  (a - b)2 + 2ab - 2b2 + b2 = a2
  
  (a - b)2 + 2ab - b= a2
  
  ∴ (a - b)2 = a2 - 2ab + b2
  
  Let us multiply the algebraic expressions and obtain the formula.
  (a - b)2 = (a - b) × (a - b)
  (a - b)2 = a (a - b) - b (a - b)
  (a - b)2 = a2 - ab - ab + b2
  (a - b)2 = a2 - 2ab + b2.
  
  ## Example
  
  Expand: (5x - 4)2
  
  (5x - 4)2
  
  = (5x)2 - 2(5x) x (4) + 42
  
  = 25x2 - 40x + 16.
  
  ## Example
  
  Expand: (98)2
  
  (98)2
  
  = (100 - 2)2
  
  = 1002 - 2 x 100 x 2 + 22
  
  = 10000 - 400 + 4
  
  = 9604.
  
  If you would like to contribute notes or other learning material, please submit them using the button below.
  
  ### Shaalaa.com
  
  Expansion of (a - b)2 = a2 - 2ab + b2 [00:02:22]
  S
  0%
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a section from a mathematics textbook or educational material, specifically for the 7th Standard of the Maharashtra State Board. It covers the expansion of the algebraic expression \((a - b)^2\). The document includes the formula, a detailed derivation, and two examples of how to apply the formula to expand specific expressions. The document does not contain a question or an answer in the form of a query or exercise.
  
  Label: no-question