Question

Pl....................................

Answer 1

$\huge\underline{Answer:-}$

$( \frac{1}{3} x - y + 5z)$

$( \frac{1}{9} {x}^{2} + {y}^{2} + 25 {z}^{2} + 5xy - \frac{5}{3} xz + 3xy)$



$\textbf{Step - By- Step - Solution:-}$


$\textbf{Using,theorm}$

${a}^{3} + {b}^{3} + {c}^{3} - 3abc$

$= (a + b + c)( {a}^{2} + {b}^{2} + {c}^{2} - ac - bc - ca)$



$\textbf{Given ,Equation}$

$\frac{1}{27 } {x}^{3} - {y}^{3} + 125 {z}^{3} + 5xyz = 0$


$\textbf{Step 1 :-}$

${ (\frac{1}{3}) }^{3} + {y}^{3} + 5 {z}^{3} + 3( \frac{1}{3}x )(y)(5z)$


$\textbf{Step 2:-}$

$( \frac{1}{3} x - y + 5z)$

[${ \: (\frac{1}{3}x) }^{2} { - (y)}^{2} + {(5z)}^{2}$

$- ( - y)(5z) - ( \frac{1}{3}x) (5z) - (\frac{1}{3} x)( - y)$]


$\textbf{Step 3:-}$

$( \frac{1}{3} x - y + 5z)$

$( \frac{1}{9} {x}^{2} + {y}^{2} + 25 {z}^{2} + 5xy - \frac{5}{3} xz + 3xy)$


$\huge\underline{Hence:-}$

Factores are

$<marquee>$
$( \frac{1}{3} x - y + 5z)$

$( \frac{1}{9} {x}^{2} + {y}^{2} + 25 {z}^{2} + 5xy - \frac{5}{3} xz + 3xy)$