Question
Factorise: 27x3 + y3 + z3 - 9xyz.
Solution
27x3 + y3 + z3 - 9xyz
= (3x)3 + (y)3 + (z)3 - 3(3x)(y)(z)
= (3x + y + z){(3x)2 + (y)2 + (z)2 - (3x)(y) - (y)(z) - (z)(3x)}
| Using Identity VIII
= (3x + y + z)(9x2 + y2 + z2 - 3xy - yz - 3zx).
