Question

(x-y)³+(y-2)³+(z-x)³​

Answer 1

Hey mate,

When a + b + c = 0 we know that a³ + b³ + c³ = 3 a b c

( x - y )³ + ( y - z )³ + ( z - x )³

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

$( = 3 xy - x z - y {}^{2}$) + yz ) ( z - x )

$( = 3 xy - x {}^{2}$y - $( - xz {}^{2}$ + $(x{}^{2}$ x - $(y) {}^{2}$ z $( xy{}^{2}$ + $( yz{}^{2}$ - xyz)

$( =3 [x{}^{2}$ ( z - y ) + $( z{}^{2}$ ( y - z ) + $( y{}^{2}$ ( x - z )]

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Similarly,

x - 2y + 2y - 3z + 3z - x = 0

Hence, ( x - 2y )³ + ( 2y - 3z )³ + ( 3z - x )³ = 3 ( x - 2y ) ( 2y - 3z ) ( 3z - x )

Hope it helps...

$( Itz ❤Aakanksha❤ here! ) {}^{}$