Question

$Factorise: 27a^3-(b-c)^3$

Answer 1

27a³-(b-c)³

a³-b³=(a-b)(a²+ab+b²)

similarly

(3a)³-(b-c)³=(3a-b+c)(9a²+3a(b-c)+(b-c)²)

=(3a-b+c)(9a²+3ab-3ac+b²+c²-2bc)

=(3a-b+c)(9a²+b²+c²+3ab-3ac-2bc)

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