Question

Factorize 9-x6+2x3y3-y6

Answer 1

Answer:

$\bold\red{(3 + {x}^{3} - {y}^{3} )(3 - {x}^{3} + {y}^{3} )}$

Step-by-step explanation:

Given,

$9 - {x}^{6} + 2 {x}^{3} {y}^{3} - {y}^{6}$

Further simplifying,

we get,

$= 9 - ( {x}^{6} - 2 {x}^{3} {y}^{3} + {y}^{6} ) \\ \\ = 9 - ( { ({x}^{3} )}^{2} - 2( {x}^{3} )( {y}^{3} ) + { ({y}^{3}) }^{2} )$

But,

we know that,

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

Therefore,

we get,

$= 9 - {( {x}^{3} - {y}^{3} ) }^{2} \\ \\ = {(3)}^{2} - {( {x}^{3} - {y}^{3} )}^{2}$

But,

we know that,

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

Hence,

we get,

$= \bold{(3 + {x}^{3} - {y}^{3} )(3 - {x}^{3} + {y}^{3} )}$