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Question

Factorise:

(x-3y)3+(3y-7z)3+(7z-x)3

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Solution

We have to factorize,
(x − 3y)3 + (3y − 7z)3 + (7z − x)3
.Let a = x − 3y ; b = 3y − 7z ; c = 7z − x
now, a + b + c = (x − 3y) + (3y − 7z) + (7z − x) = 0
Since, a + b + c = 0, then we have


a cubed plus b cubed plus c cubed equals 3 a b c left parenthesis x space minus space 3 y right parenthesis 3 space plus space left parenthesis 3 y space minus space 7 z right parenthesis 3 space plus space left parenthesis 7 z space minus space x right parenthesis 3 space equals space 3 left parenthesis x space minus space 3 y right parenthesis left parenthesis 3 y space minus space 7 z right parenthesis left parenthesis 7 z space minus space x right parenthesis

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