Question

please help me out !!​

Answer 1

AnsweR :

Option ( b )

$\sf \bold{(x - y)(y - z)(z - x)}$

SolutioN :

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

$\sf = {x}^{2} y - {x}^{2} z + {y}^{2} z - {y}^{2} x + {z}^{2} x - {z}^{2} y$

$\sf = {x}^{2} y - {x}^{2} z - {y}^{2} x + {z}^{2} x + {y}^{2} z - {z}^{2} y$

$\sf = {x}^{2} (y - z) - x( {y}^{2} - {z}^{2} ) + yz(y - z)$

$\sf = {x}^{2} (y - z) - x(y - z)(y + z) + yz(y - z)$

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

$\sf = (y - z)[ {x}^{2} - xy - xz + yz]$

$\sf = (y - z)[x(x - y) - z(x - y)]$

$\sf = (y - z)( x - y)(x - z)$

or

$\sf = (x - y)(y - z)(z - x)$

Answer 2

Answer:

option B is the correct answer