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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