Factorise: 27x^3+y^3+z^3–9xyz

27x3+y3+z3–9xyz 

Solution:

The expression27x3+y3+z3–9xyz can be written as (3x)3+y3+z3–3(3x)(y)(z)

27x3+y3+z3–9xyz  = (3x)3+y3+z3–3(3x)(y)(z)

We know that, x3+y3+z3–3xyz = (x+y+z)(x2+y2+z2–xy –yz–zx)

27x3+y3+z3–9xyz  = (3x)3+y3+z3–3(3x)(y)(z)

= (3x+y+z)[(3x)2+y2+z2–3xy–yz–3xz]

= (3x+y+z)(9x2+y2+z2–3xy–yz–3xz)