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Factorise a 3 – 27b 3 – 7ab 2 + 21a 2 b

Factorise a3 – 27b3 – 7ab2 + 21a2b

Grade:12th pass

1 Answers

MANU MITRAAN
22 Points
9 years ago
Divide by b3 and replace (a/b) by x ;
we get,
  x3 + 21x2 _ 7x –27 = 0;
Notice if x =  -1 then it reduces to 0;
.: (x+1) is a factor ;
Now divide the equation by (x+1) 
we get, x2 + 20x – 27 which cannot be reduced as it has complex roots;
 Hence the original equation is :
  (x+1)(x2+20x-27)
  replacing x=a/b we get
(a/b+1)((a/b)3 +20(a/b) -27)
which is the following:
 
(a+b)(a3 +20ab2 -27b3)
 
   is the required answer!!
 
 
 

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