We have, a 3 (b – c) 3 + b 3 (c – a) 3 + c 3 (a – b) 3 We know that, a 3 + b 3 + c 3 – 3abc = (a + b + c) (a 2 + b 2 + c 2 – ab – bc – ca)] Also, If, (x + y + z) = 0 Then (x 3 + y 3 + z 3 ) = 3xyz Given, x + y + 4 = 0 We have, (x 3 + y 3 – 12xy + 64) = (x) 3 + (y) 3 + (4) 3 – 3 (x) (y) (4) = 0

If find the value of

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

Given,

x + y + 4 = 0

We have,

(x³ + y³ – 12xy + 64)

= (x)³ + (y)³ + (4)³ – 3 (x) (y) (4) = 0