Question

factories a³(b-c)³+b³(c-a)³+c³(a-b)³​

Answer 1

Answer:

Consider, c³(a−b)³+a³(b−c)³+b³(c-a)³

= (ac − bc)³ + (ab − ac)³+ (bc - ab)³

Consider, x = (ac − bc), y = (ab − ac) and z = (bc - ab)

⇒ x + y + z = (ac − bc) + (ab − ac) + (bc - ab) = 0

If x + y + z = 0 then x3 + y3 + z3 = 3xyz

Hence (ac − bc)³ + (ab − ac)³+ (bc - ab)³ = 3(ac − bc)(ab − ac)(bc - ab)

= 3c(a − b) × a(b − c) × b(c - a)

= 3abc(a − b)(b − c)(c - a)