Question

if x+y+z=0,then facorize (x+y-z)3 +(x-y+z)3 - (x-y-z)3​

Answer 1

Answer:

9x-3y-3z

Step-by-step explanation:

Answer 2

The value of $( x + y - z)^{3}$ + $( x - y + z)^{3}$ - $( x - y - z)^{3}$ = - 24xyz.

Step-by-step explanation:

Given,

x + y + z = 0  .... (1)

∴ $( x + y - z)^{3}$ + $( x - y + z)^{3}$ - $( x - y - z)^{3}$

= $( - z - z)^{3}$ + $( - y - y )^{3}$ - $( x + x)^{3}$

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

[∵ $x^{3}$ + tex]y^{3}[/tex] + tex]z^{3}[/tex] = 3xyz]

∴ $( - 2z)^{3}$ + $( - 2y  )^{3}$ - $( 2x )^{3}$

= 3(- 2z)(- 2y)(- 2x)

= - 24xyz

Hence, $( x + y - z)^{3}$ + $( x - y + z)^{3}$ - $( x - y - z)^{3}$ = - 24xyz.