Question

factorise 8x^3+y^3+z^3-6xyz using identity
​

Answer 1

$\textbf{Given:}$

$8x^3+y^3+z^3-6\,xyz$

$\textbf{To find:}$

$\text{Factors of 8x^3+y^3+z^3-6\,xyz }$

$\textbf{Solution:}$

$\text{Consider,}$

$8x^3+y^3+z^3-6\,xyz$

$=(2x)^3+y^3+z^3-3(2xyz)$

$\text{We know that the identity}$

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

$\text{we get}$

$=(2x+y+z)((2x)^2+y^2+z^2-2xy-yz-2xz)$

$=(2x+y+z)(4x^2+y^2+z^2-2xy-yz-2xz)$

$\therefore\bf\,8x^3+y^3+z^3-6\,xyz=(2x+y+z)(4x^2+y^2+z^2-2xy-yz-2xz)$

Find more:

Factorise the following by using a suitable identity :a3+b3-8c3+6abc

https://brainly.in/question/3887522

If X + Y + Z = 6 and X square + Y square + Z square = 18 then find x cube + y cube + Z cube - 3 x y z​

https://brainly.in/question/15081719#