Question

Factorise :(x-2y)³ + ( 2y - 3z )³ + ( 3z - x )³

Answer 1

Solution :

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We know that,

If a+b+c=0 then

a³ + b³ + c³ = 3abc

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Here ,

a = x-2y, b = 2y-3z , c = 3z-x

Now ,

a+b+c

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

= 0

Therefore ,

a³ + b³ + c³

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

= 3(x-2y)( 2y - 3z )( 3z - x )

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