Factorize: (5a – 7b) 3 + (9c – 5a) 3 + (7b – 9c) 3

Question

Factorize: (5a &#x2013; 7b) 3 + (9c &#x2013; 5a) 3 + (7b &#x2013; 9c) 3

Philoid · Accepted Answer

We have,

a³ (b – c)³ + b³ (c – a)³ + c³ (a – b)³

We know that,

a³ + b³ + c³ – 3abc = (a + b + c) (a² + b² + c² – ab – bc – ca)]

Also,

If, (x + y + z) = 0

Then (x³ + y³ + z³) = 3xyz

Since,

(5a – 7b) + (9c – 5a) + (7b – 9c) = 5a – 7b + 9c – 5a + 7b – 9c = 0

Therefore,

(5a – 7b)³ + (9c – 5a)³ + (7b – 9c)³ = 3 (5a – 7b) (9c – 5a) (7b – 9c)