Question

Q. Factorise : 27 x³ + y³ + z³ – 9xyz.​

Answer 1

The factorise are the from of 2=2×1 are the formula of factorise

Step-by-step explanation:

27×27×27+y+y+y+z+z+z

729×27+y+y+y+z+z+z

19283+y+y+y+z+z+z

19283yz÷(-9xyz)

=2142 xyz Ans.

Answer 2

$\rm \red{27 x³ + y³ + z³ – 9xyz} \\ \rm \red{ = (3x {)}^{3} + (y {)}^{3} + {(z)}^{3} - 9xyz } \\ \rm \red{ = (3x {)}^{3} + {(y)}^{3} + {(z)}^{3} - 3 \times 3x \times y \times z}$

$\color{blue}{ \boxed{\begin{matrix} \rm Using \: identity : \\ \rm {a}^{3} + {b}^3 + {c}^{3} - 3abc = (a + b + c)( {a}^{2} + {b}^{2} + {c}^2 - ab - bc - ca) \\ \rm putting \: a = 3x, \: b = y , \: c = z\end{matrix}}}$

$\rm\color{green} =(3x + y + z)(9 {x}^{2} + {y}^{2} + {z}^{2} - 3xy - yz - 3zx)$