Question:গুণ কর:

 ক. `(9x^2y^2)/(7y^2z^2), (5b^c^2)/(3z^2x^2)` এবং `(7c^2a^2)/(x^2y^2)`

 খ. `(16a^2b^2)/(21z^2), (28z^4)/(9x^3y^4)` এবং `(3y^7z)/(10x)`

 গ. `(yz)/x^2, (zx)/y^2,` এবং `(xy)/z^2`

 ঘ. `(x - 1)/(x + 1), (x - 1)^2/(x^2 + x)` এবং `x^2/(x^2 - 4x + 5)`

 ঙ. `(x^4 - y^4)/(x^2 - 2xy + y^2), (x - y)/(x^3 + y^3)` এবং `(x + y)/(x^3 + y^3)`

 চ.`(1 - b^2)/(1 + x),(1 - x^2)/(b + b^2)` এবং `(1 + (1 - x)/x)`

 ছ.`(x^2 - 3x + 2)/(x^2 - 4x + 3), (x^2 - 5x + 6)/(x^2 - 7x + 12)` এবং `(x^2 - 16)/(x^2 - 9)`

 জ.`(x^3 + y^3)/(a^2b + ab^2 + b^3), (a^3 - b^3)/(x^2 - xy + y^2)` এবং `(ab)/(x + y)`
 
 ঝ.` (x^3 + y^3 + 3xy (x + y))/(a + b)^3, (a^3 + b^3 + 3ab (a + b))/(x^2 - y^2)` এবং `(x - y)^2/(x + y)^2` 

Answer ক. নির্ণেয় গুণফল

    `= (9x^2y^2)/(7y^2z^2) xx (5b^c^2)/(3z^2x^2) xx (7c^2a^2)/(x^2y^2)`

     `= (9x^2y^2 xx 5b^2c^2 xx 7c^2a^2)/(7y^2z^2 xx 3z^2x^2 xx x^2y^2)`

    ` = (15a^2b^2c^4)/(x^2y^2z^4)`

       উত্তর: `(15a^2b^2c^4)/(x^2y^2z^4)`


  খ. নির্ণেয় গুণফল

   `= (16a^2b^2)/(21z^2) xx (28z^4)/(9x^3y^4) xx (3y^7z)/(10x)`

   `= (16a^2b^2 xx 28z^4 xx 3y^2z)/(21z^2 xx 9x^3y^4 xx 10x)`

   `= (16 xx 28 xx 3 xx a^2b^2y^7z^5)/(21 xx 9 xx 10 xx x^4y^4z^2)`

   `= (32a^2b^2y^3z^3)/(45x^4)` 

    উত্তর:` (32a^2b^2y^3z^3)/(45x^4)` 


 গ. নির্ণেয় গুণফল
   
    `= (yz)/x^2 xx (zx)/y^2 xx (xy)/z^2`

    `= (x^2y^2z^2)/(x^2y^2z^2)`

      = 1

      উত্তর: 1

 ঘ.   নির্ণেয় গুণফল
   
     `= (x - 1)/(x + 1) xx (x - 1)^2/(x^2 + x) xx x^2/(x^2 - 4x + 5)`

     `= (x - 1)/(x + 1) xx ((x - 1) (x - 1))/(x (x + 1)) xx x^2/(x^2 - 4x + 5)`

     `= (x (x - 1))^3/((x + 1)^2 (x^2 - 4x + 5))`

     উত্তর: `(x (x - 1))^3/((x + 1)^2 (x^2 - 4x + 5))`


 ঙ.  নির্ণেয় গুণফল

  `= (x^4 - y^4)/(x^2 - 2xy + y^2) xx (x - y)/(x^3 + y^3) xx (x + y)/(x^3 + y^3)`

  `= ((x^2 + y^2) (x^2 - y^2))/(x - y)^2 xx (x - y)/((x + y) (x^2 - xy + y^2)) xx (x + y)/((x + y) (x^2 - xy + y^2))`

   `= ((x^2 + y^2) (x + y) (x - y))/((x - y) (x - y)) xx (x - y)/((x + y) (x^2 - xy + y^2)) xx (x + y)/((x + y) (x^2 - xy + y^2))`

   `= (x^2 + y^2)/(x^2 - xy + y^2)^2`

      উত্তর:` (x^2 + y^2)/(x^2 - xy + y^2)^2`

 চ.নির্ণেয় গুণফল
 
   `= (1 - b^2)/(1 + x) xx (1 - x^2)/(b + b^2) xx (1 + (1 - x)/x)`

   `= ((1 + b) (1 - b))/(1 + x) xx ((1 + x) (1 - x))/(b (1 + b)) xx (x + 1 - x)/x`

   `= ((1 - b) (1 - x))/b xx 1/x`

   `= ((1 - b) (1 - x))/(bx)`

      উত্তর:` ((1 - b) (1 - x))/(bx)`


 ছ. নির্ণেয় গুণফল

   `= (x^2 - 3x + 2)/(x^2 - 4x + 3) xx (x^2 - 5x + 6)/(x^2 - 7x + 12) xx (x^2 - 16)/(x^2 - 9)`

   `= (x^2 - 2x - x + 2)/(x^2 - 3x - x + 3) xx (x^2 - 3x - 2x + 6)/(x^2 - 4x - 3x + 12) xx (x^2 - 4^2)/(x^2 - 3^2)`

   `= (x(x - 2) - 1(x - 2))/(x(x - 3) - 1(x - 3)) xx (x(x - 3) - 2(x - 3))/(x(x - 4) - 3 (x - 4)) xx ((x + 4) (x - 4))/((x + 3) (x - 3))`

   `= ((x - 2) (x - 1))/((x - 3) (x - 1)) xx ((x - 3) (x - 2))/((x - 4)(x - 3)) xx ((x + 4) (x - 4))/((x + 3) (x - 3))`

   `= ((x - 2) (x - 2) (x + 4))/((x - 3)(x + 3)(x - 3))`

   `= ((x - 2)^2 (x + 4))/((x - 3)^2 (x + 3))`

     উত্তর: ` ((x - 2)^2 (x + 4))/((x - 3)^2 (x + 3))`

 জ. নির্ণেয় গুণফল

   `= (x^3 + y^3)/(a^2b + ab^2 + b^3) xx (a^3 - b^3)/(x^2 - xy + y^2) xx (ab)/(x + y)`

   `= ((x + y)(x^2 - xy + y^2))/(b(a^2 + ab + b^2)) xx ((a - b) (a^2 + ab + b^2))/(x^2 - xy + y^2) xx (ab)/(x + y)`

   `= a (a - b)`

     উত্তর:` a (a - b)`
 
 ঝ. নির্ণেয় গুণফল

  ` = (x^3 + y^3 + 3xy (x + y))/(a + b)^3 xx (a^3 + b^3 + 3ab (a + b))/(x^2 - y^2) xx ((x - y))^2/((x + y))^2`

   `= (x^3 + y^3 + 3x^2y + 3xy^2)/(a + b)^3 xx (a^3 + b^3 + 3a^2b + 3ab^2)/(x^2 - y^2) xx (x - y)^2/(x + y)^2`

   `= (x + y)^3/(a + b)^3 xx (a + b)^3/((x + y) (x - y)) xx (x - y)^2/(x + y)^2`

   `= ((x + y)^3 xx (a + b)^3 xx (x - y)^2)/((x + y)^3 xx (a + b)^3 xx (x - y))`

     = (x - y)

     উত্তর: (x - y) 

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