Question

Factorise: 27x${}^3$+y${}^3$+2y${}^3$-9xyz

Answer 1

$27x^3+y^3+z^3-9xyz$

$={\left(3x\right)}^3+y^3+z^3-3\times \left(3x\right)\times y\times z$

$=[3x+y+z][{\left(3x\right)}^2+y^2+z^2-(3x)\times y-y\times z-z(3x\left)\right]$ [Since $a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)$]

$=[3x+y+z][9x^2+y^2+z^2-3xy-yz-3zx]$