Question

factorise : x²-y²+2yz-z²​

Answer 1

Answer:

( x + y − z ) ( x − y + z )

Step-by-step explanation:

a^2 − b ^2 = ( a + b ) ( a − b )  

where  a = x  and  b = y − z .

( x + y − z ) ( x − y + z )

Answer 2

Given,

$x^{2} -y^{2} +2yz-z^{2}$

Take $-$ as common

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

$(y^{2}+z^{2}-2zy )$ is same like $(a-b)^{2}=a^{2} +b^{2}-2ab$ form

So, we can write,

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

$x^{2} -(y-z)^{2}$

$x^{2} -(y-z)^{2}$ is same like $x^{2} -y^{2}$ form

Formula,

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

So, we can write

$(x-y+z)(x+y-z)$

Therefore, the factors of $x^{2} -y^{2}+2yz-z^{2}$ is $(x-y+z)(x+y-z)$.