Question

(27x)³+(y)³+(z)³-9xyz
Factorize

Answer 1

Given: 27x3 + y3 + z3 - 9xyz

⇒ 27x3 + y3 + z3 - 9xyz

= (3x)3 + y3 + z3 - 3(3x)(y)(z)

= (3x + y + z )[(3x)2 + y2 + z2 - (3x) × y − y × z − z(3x)] [ ∵ a2 + b3 + c3 = (a + b + c )(a2 + b2 + c2 - ab−bc−ca) ] = (3x + y + z )(9x2 + y2 + z2 - 3xy − yz − 3zx)