Question

Factorize $\frac{1}{27}{x}^3-y^3+125z^3+5xyz$

Answer 1

$\frac{1}{27}{x}^3-y^3+125z^3+5xyz={\left(\frac{1}{3}x\right)}^3+(-y{)}^3+(5z{)}^3-3\times \frac{x}{3}\times x(-y)\times 5z=(\frac{1}{3}x-y+5z)[{\left(\frac{1}{3}x\right)}^2+(-y{)}^2+(5z{)}^2-\frac{1}{3}x(-y)-(-y)\times 5z-5z\times \frac{1}{3}x]=(\frac{1}{3}x-y+5z)(\frac{1}{9}{x}^2+y^2+25z^2+\frac{1}{3}xy+4yz-\frac{5}{3}zx)$