Question

[(a2-b2)3 +(b2-c2)3 +(c2-a2)3]divided by / (a-b)3+(b-c)3+(c-a)3

Answer 1

Heya user,

We know,
---> if a + b + c = 0 ; a³ + b³ + c³ = 3abc

We observe,
( a² - b² ) + ( b² - c² ) + ( c² - a² ) = 0
=> ( a² - b² )³ + ( b² - c² )³ + ( c² - a² )³ = 3( a² - b² )( b² - c² )( c² - a² )

Similarly, 
( a - b ) + ( b - c ) + ( c - a ) = 0
=> ( a - b )³ + ( b - c )³ + ( c - a )³ = 3( a - b )( b - c )( c - a )

Now, [ ( 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 ) <---- Answer...

Answer 2

HEYA ❣❣❣

hope this is helpful for you.

thank you very much.

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