Question

Factorize (x² + y² -z²)²-4x²y²

Answer 1

SOLUTION

TO FACTORISE

$\sf{ {( {x}^{2} + {y}^{2} - {z}^{2} )}^{2} - 4 {x}^{2} {y}^{2} }$

EVALUATION

Here the given expression is

$\sf{ {( {x}^{2} + {y}^{2} - {z}^{2} )}^{2} - 4 {x}^{2} {y}^{2} }$

We factorise it as below

$\sf{ {( {x}^{2} + {y}^{2} - {z}^{2} )}^{2} - 4 {x}^{2} {y}^{2} }$

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

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

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

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

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

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Answer 2

Answer:

thank u for answer please do it properly