Factorise completely

1.	Factorise completely
Answer» ong>ANSWER: $( {(xy)}^{2} + {z}^{2} )(xy + z)(xy - z)$ Step-by-step explanation: *Given* *QUESTION, To factorise, ${(xy)}^{4} - {z}^{4}$ Solution: ${(xy)}^{4} - {z}^{4}$ $= {({(xy)}^{2}) }^{2} - {( {z}^{2} )}^{2}$ Since, ${a}^{2} - {b}^{2} = (a + b)(a - b)$ Hence, $( {(xy)}^{2} + {z}^{2} )( {(xy)}^{2} - {z}^{2} )$ $( {(xy)}^{2} + {z}^{2} )( {(xy)}^{2} - {(z)}^{2} )$ Since, ${a}^{2} - {b}^{2} = (a + b)(a - b)$ Hence, $( {(xy)}^{2} + {z}^{2} )(xy + z)(xy - z)$ RESULT: Hence, the* *REQUIRED* *factorise* *form* is, $( {(xy)}^{2} + {z}^{2} )(xy + z)(xy - z)(ans)$

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