Question

I need to solve these questions of maths they are of factorise

Answer 1

 a)  Let ( a-b ) = x , ( b-c ) = y , ( c-a ) = z     = x cube + y cube = z cube where, ( x + y + z )     = ( a-b ) + ( b-c ) +  (c-a )
     = a - b + b - c + c - a     = 0 = 3xyz     =  3 ( a-b ) ( b-c ) (c-a)
( If x + y + z = 0 , then cube + y cube + z cube = 3xyz )
b) Let ( 3a - 2b ) = x , ( 2b - 5c ) = y , ( 5c - 3a) = z     = x cube + y cube  + z cube where ( x + y + z )     = ( 3a - 2b ) + ( 2b - 5c ) + ( 5c - 3a )     = 3a - 2b + 2b - 5c + 5c - 3a     = 0 = 3xyz     = 3 ( 3a - 2b ) ( 2b - 5c ) ( 5c - 3a )( If ( x + y+ z ) = 0 , then x cube + y cube + z cube = 3xyz ) 
c ) Let  a ( b-c ) = x , b ( c-a ) = y ,  c ( a-b ) = z     Here, x + y + z  = a ( b-c ) + b ( c-a ) + c ( a -b )                               = ab - ac + bc - ba + ca - cb  = 0                               = 3xyz                               = 3abc ( b-c ) ( c-a ) ( a-b )
Since x + y + z = 0 , then x cube + y cube + z cube = 3xyz
d)  Let
( 5a - 7b ) = x ,  ( 9c - 5a ) = y , ( 7b - 9c ) = z where ,  x + y + z =   (5a - 7b )  + ( 9c - 5a ) + ( 7c - 9a )                            = 5a - 7b + 9c - 5a + 7b - 9c                            = 0                            = 3xyz                            = 3 ( 5a - 7b ) ( 9c - 5a ) ( 7b - 5a )( If  (x + y + z ) = 0 , then x cube + y cube +  z cube = 3xyz )