Question

factorize :27×3 + y3 + z3 -9xyz

Answer 1

Given


p(x) = 27x³ + y³ + z³ - 9xyz.


To factorise the given polynomial

Here, we observe that

27x³ = (3x)³

y³ = (y)³ and z³ = (z)³

-9xyz = -3(3x)(y)(z)


So, we know that,

a³ + b³ + c³ - 3abc =

(a + b + c)(a² + b² + c² - ab - bc - ca)

Hence,

27x³ + y³ + z³ - 9xyz =

(3x + y + z){(3x)² + y² + z² - (3x)(y) - (3x)(z) - (y)(z)}

= (3x + y + z)(9x² + y² + z² - 3xy - 3xz - yz)


Answer :- (3x + y + z)(9x² + y² + z² - 3xy - 3xz - yz)