Q. 53.9( 12 Votes )

Let us factorise the following algebraic expressions:

(3a – 2b)3 + (2b – 5c)3 + (5c – 3a)3

Answer :

Let us consider (3a - 2b) = x, (2b - 5c) = y, (5c - 3a) = z


So x + y + z = 3a – 2b + 2b – 5c + 5c – 3a = 0


(3a – 2b) 3 + (2b – 5c) 3 + (5c – 3a) 3 = x3 + y3 + z3


Since x + y + z = 0, hence


x3 + y3 + z3 = 3xyz


(3a – 2b) 3 + (2b – 5c) 3 + (5c – 3a) 3 = 3×(3a – 2b)×(2b – 5c)× (5c – 3a)


3(3a – 2b) (2b – 5c) (5c – 3a)


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