Factorize: (3a – 2b) 3 + (2b – 5c) 3 + (5c – 3a) 3

Question

Factorize: (3a &#x2013; 2b) 3 + (2b &#x2013; 5c) 3 + (5c &#x2013; 3a) 3

Philoid · Accepted Answer

We know that,

If, (x + y + z) = 0

Then (x³ + y³ + z³) = 3xyz

We have,

(3a – 2b) (2b – 5c) + (5c – 3a) = 0

So,

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

Factorize:(3a – 2b)3 + (2b – 5c)3 + (5c – 3a)3