Question

factories the following. ​

Answer 1

Answer :

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

Explanation :

( x² - 2xy + y² ) - z²

we know that, ( x - y )² = x² - 2xy + y²

•°• ( x² - 2xy + y² ) = ( x - y )²

=> ( x - y ) ² - ( z )²

We also know that, ( a² - b² ) = ( a + b ) ( a - b )

=> [ ( x - y ) + z ] [ ( x - y ) - z ]

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

Hence, required expression is factorised.

Answer 2

Question:

Factorise the given expression

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

Answer:

$\large\boxed{\sf{(x-y+z)(x-y-z)}}$

Step-by-step explanation:

Given expression

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

Further solving, we get

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

Concept Map:

• ${(a - b)}^{2} = {a}^{2} - 2ab + {b}^{2}$

• ${a}^{2} - {b}^{2} = (a + b)(a - b)$