Question

Factorise : x3 - 27y3 + 8z+ 18xyz.​

Answer 1

$<b><marquee><font color="blue">SEE THE ATTACHMENT FOR THE ANSWER$

Answer 2

Correct question:

$\sf{}Factorise:$

$\sf{}x^3 +27y^3 +8z^3-18xyz$

Answer:

$\sf{}(x+3y+2z)(x^2+9x^2+4z^2-3xy-6yz-2zx)$

Explanation:

We know:-

$\sf{}a^3+b^3+c^3-3abc= (a+b+c)(a^2+b^2+c^2-ab-bc-ca)$

$\sf{}x^3 +27y^3 +8z^3-18xyz$

Here,

a => x

b => 3y

c => 2z

$\implies \sf{}(x)^3 +(3y)^3 +(2z)^3-3(x)(3y)(2z)$

$\implies \sf{}(x+3y+2z)[(x)^2+(3y)^2+(2z)^2-(x)(3y)-(3y)(2z)-(2z)(x)]$

$\implies \sf{}(x+3y+2z)[(x)^2+(3y)^2+(2z)^2-3xy-6yz-2zx]$

$\therefore \sf{}(x+3y+2z)(x^2+9x^2+4z^2-3xy-6yz-2zx)$

Know more

$1)\sf{}(a+b)^2= a^2+b^2+2ab$

$2)\sf{}(a-b)^2= a^2+b^2-2ab$

$3)\sf{}(a-b)^3= a^3-b^3-3ab(a-b)$

$4)\sf{}(a+b)^3= a^3+b^3+3ab(a+b)$

$5)\sf{}a^2-b^2=(a-b)(a+b)$