Question

Factorize 27x³+y³+z³-9xyz​

Answer 1

Given that : -

• 27x³ + y³ + z³ - 9xyz

Solution :-

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

$\blue {{\qquad \underline{\large \bf \underline{using \: \: \: identity : - }}}}$

$\red{ \sf \: a³ + b³ + c³ - 3abc =} \\ \red{\sf \: (a+b+c)(a²+b²+c²-ab-bc-ca)}$

$\sf \qquad \qquad \blue{putting a=3x, b=y, c=z}$

$\tt \red\longrightarrow(3x + y + z)(9x ^{2} + {y}^{2} + {z}^{2} - 3xy - { {y}^{2} } - 3zx )$

Answer 2

Step-by-step explanation:

27x³ + y³ + z³– 9xyz

= (3x)^3 + (ʏ)^3 + (ᴢ)^3 - 9xʏᴢ

=(3x)^3 + (ʏ)^3 + (ᴢ)^3 - 3 × 3x × Y × Z

Usɪɴɢ ɪᴅᴇɴᴛɪᴛʏ 8:

a^3 + b^3 + c^3 -3ab =

( a+b+c) (a^2+b^2+c^2 - ab - bc - ca )

[ PUTTING a= 3x , b = y , c= z ]

= (3x + y +z ) ( 9x^2 +y^2 +z^2 -3xy - yz -3zx

Fɪɴᴀʟʟʏ ᴅᴏɴᴇ !..