Question

Factorise completely
$(xy) ^{4} - z ^{4}$
​

Answer 1

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,

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