Question

(a²-b²)³+(b²-c²)³+(c²-a²)³÷(a-b)³+b-c)³+(c-a)³=​

Answer 1

Answer:

we use the fact that if a+b+c = 0, then a³+b³+ c³ = 3 a b c.

(a² - b²) + (b² - c²) + (c² - a²) = 0...

also (a-b) + (b-c)+ (c-a) = 0

we assume that a ≠b ≠ c.

hence,

(a²-b²)³+(b²-c²)³+(c²-a²)³ ÷ (a-b)³+b-c)³+(c-a)³

= 3 (a² - b²) (b² - c²) (c² - a²) / [ 3 (a - b) (b - c) ( c -a) ]

= ( a+b) (b + c) ( c +a)

∵ a² - b² = (a -b) (a+b) and similarly other terms.