CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

Simplify : 

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


Solution

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.
 

flag
 Suggest corrections
thumbs-up
 
2 Upvotes


Similar questions
View More


People also searched for
View More



footer-image