Question

Pls help me with question no.3

Answer 1

Please put the identity A3 +B3 + C3=(a+b+c)(A2+B2+C2-ab-bc-ca)

Answer 2

Q. Find the value of :

( x - y )³ + ( y - z )³ + ( z - x )³

Solution :

Let, ( x - y ) = A --------- ( 1 )

( y - z ) = B ----------- ( 2 )

( z - x ) = C --------- ( 3 )

Adding ( 1 ) , ( 2 ) and ( 3 ),

⇒ x - y + y - z + z - x = A + B + C


⇒ 0 = A + B + C

Now,

= A³ + B³ + C³

Using identity,

[ If , ( A + B + C = 0 ),then ( A³ + B³ + C³ = 3ABC ]

= 3ABC

Substitute the value of A , B and C.

= 3( x - y ) ( y - z ) ( z - x ).

The required factorisation is [ 3( x - y )( y - z )( z - x ) ].