Factorize 27x³+y³+z³-9xyz

1.	Factorize 27x³+y³+z³-9xyz
Answer» GIVEN that : - 27x³ + y³ + z³ - 9xyz Solution :- $\tt\red\longrightarrow \: {(27x)}^{3} + {y}^{3} + {z}^{3} - 9xyz \\ \\ \\ \tt\red\longrightarrow {(3x)}^{3} + ( {y)}^{3} + {(2)}^{3} - 9xyz \\ \\ \\ \tt\red\longrightarrow {(3x)}^{3} + {(y) }^{3} + {(2)}^{3} - 3 \times 3x \times y \times z$ $\blue {{\qquad \underline{\large \bf \underline{using \: \: \: identity : - }}}}$ $\red{ \sf \: a³ + b³ + c³ - 3abc =} \\ \red{\sf \: (a+b+c)(a²+b²+c²-ab-bc-ca)}$ $\sf \qquad \qquad \blue{putting a=3x, b=y, c=z}$ $\tt \red\longrightarrow(3x + y + z)(9x ^{2} + {y}^{2} + {z}^{2} - 3xy - { {y}^{2} } - 3zx )$

Answer»

GIVEN that : -

27x³ + y³ + z³ - 9xyz

Solution :-

$\tt\red\longrightarrow \: {(27x)}^{3} + {y}^{3} + {z}^{3} - 9xyz \\ \\ \\ \tt\red\longrightarrow {(3x)}^{3} + ( {y)}^{3} + {(2)}^{3} - 9xyz \\ \\ \\ \tt\red\longrightarrow {(3x)}^{3} + {(y) }^{3} + {(2)}^{3} - 3 \times 3x \times y \times z$