Question:দুইটি রাশির  বর্গের অন্তররুপে প্রকাশ কর:

 ক.(5p - 3q) (p + 7q)

 খ. (6a + 9b) (7b - 8a)

 গ. (3x + 5y) (7x - 5y)

 ঘ. (5x + 13) (5x - 13) 

Answer ক. ‍(5p - 3q) (p + 7q)

আমরা জানি, 
   ab =` ((a + b)/2)^2 - ((a - b)/2)^2`

   :. (5p - 3q) (p + 7q)

  `= {((5p - 3q) + (p + 7q))/2}^2 - {((5p - 3q) - (p + 7q))/2}^2`

  `= ((5p - 3q + p + 7q)/2)^2 - ((5p - 3q - p - 7q)/2)^2`

  `= ((6p + 4q)/2)^2 - ((4p - 10q)/2)^2`

  `= {(2(3p + 2q))/2}^2 - {(2(2p - 5q))/2}^2`

  `= (3p + 2q)^2 - (2p - 5q)^2`

  উত্তর: `(3p + 2q)^2 - (2p - 5q)^2`


  খ.(6a + 9b) (7b - 8a) 

আমরা জানি,

    ab =` ((a + b)/2)^2 - ((a - b)/2)^2`

    :. (6a + 9b) (7b - 8a)

    = `{((6a + 9b) + (7b - 8a))/2)^2 - {((6a + 9b) - (7b - 8a))/2}^2`

    = `((6a + 9b + 7b - 8a)/2)^2 - ((6a + 9b - 7b + 8a)/2)^2`

    =` ((16b - 2a)/2)^2 - ((2b + 14a)/2)^2`

    =` {(2(8b - a))/2}^2 - {(2(b + 7a))/2}^2`

    =` (8b - a)^2 - (b + 7a)^2`

     উত্তর: ` (8b - a)^2 - (b + 7a)^2`


 গ. (3x + 5y) (7x - 5y) 

আমরা জানি,

   ab =` ((a + b)/2)^2 - ((a - b)/2)^2`

   :. (3x + 5y) (7x - 5y)

   =` {((3x + 5y) + (7x - 5y))/2}^2 - {((3x + 5y) - (7x - 5y))/2}^2`

   =` ((3x + 5y + 7x - 5y)/2)^2 - ((3x + 5y - 7x + 5y)/2)^2`

   =` ((10x)/2)^2 - ((- 4x + 10y)/2)^2`

   =` (5x)^2 - {(- 2 (2x - 5y))/2}^2`

   =` (5x)^2 - (2x - 5y)^2`

   = `(5x)^2 - (2x - 5y)^2`

     উত্তর: `(5x)^2 - (2x - 5y)^2`

  ঘ. (5x + 13) (5x - 13)

আমরা জানি,

   ab = `((a + b)/2)^2 - ((a - b)/2)^2`

   :. (5x + 13) (5x - 13)

   =` {((5x + 13) + (5x - 13))/2}^2 - {((5x + 13) - (5x - 13))/2}^2`

   =` ((5x + 13 + 5x - 13)/2)^2 - ((5x + 13 - 5x + 13)/2)^2`

   =` ((10x)/2)^2 - ((26)/2)^2`

   = `(5x)^2 - (13)^2`

    উত্তর:  `(5x)^2 - (13)^2` 

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