Question

Factorise: x^2+ y^2- z^2 - 2 xy​

Answer 1

Step-by-step explanation:

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(x 2 −2xy+y 2 )−z 2

⇒[x(x−y)−y(x−y)]−z 2

⇒(x−y)(x−y)−z 2

⇒(x−y) 2 −z 2

⇒[(x−y)+z][(x−y)−z]

⇒(x−y+z)(x−y−z)

Answer 2

Answer:

x² + y² - z² - 2xy = (x - y - z) (x - y + z)

Step-by-step explanation:

• TO FACTORISE :

x² + y² - z² - 2xy

• CONCEPT USED :

(x + y)² = x² + y² + 2xy

(x - y)² = x² + y² - 2xy

(x + y) (x - y) = x² - y²

• SOLUTION :

x² + y² - z² - 2xy

= x² + y² - 2xy - z²

= (x - y)² - z² [ ∵ (x - y)² = x² + y² - 2xy ]

= (x - y - z) {x - y - (-z)} [ ∵ (x + y) (x - y) = x² - y² ]

= (x - y - z) (x - y + z)

HOPE IT HELPS YOU !

THANKS !