1.

Factorise :- 8 + 9(a - b)6 - (a - b)12

Answer»

-8 + 9(a - b)6 - (a - b)12 

 Let (a - b)6 = x 

Then -8 + 9x - x2 = - (x2 - 9x + 8) = - (x2 - 8x - x + 8) 

= - (x - 8)(x - 1) 

 = - [(a - b)6 - 8][(a - b)6 - 1] 

 = [1 - (a - b)6 ][(a - b)6 - 8] 

 = [(1)3 - {(a - b)2 } 3 ][{(a - b)2 } 3 - (2)3 ] 

 = [1 - (a - b)2 ][1 + (a - b)4 + (a - b)2 ][(a - b)2 - 2][(a - b)4 + 4 + 2(a - b)2]

 


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