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Factorize: (i) 9-a^6+2a^3b^3-b^6 (ii)...

Factorize:
(i) `9-a^6+2a^3b^3-b^6`
(ii)`x^(16)-y^(16)+x^8+y^8`

Text Solution

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(i) `9-a^6+2a^3b^3-b^6`
`= 9 - (a^6 - 2a^3b^3 + b^6 )`
`=32 - ( a^3 - b^3 )2`
`=(3 - ( a^3 - b^3 )) ( 3 + ( a^3 - b^3 ))`
`=(3 - a^3 +b^3 )( 3 + a^3 - b^3)`

(ii)`x^(16)-y^(16)+x^8+y^8`
`=(x^8)^2-(y^8)^2`
`=(x^8+y^8)(x^4+y^4)(x^4-y^4)`
`=(x^8+y^8)(x^4+y^4)(x^2+y^2)(x+y)(x-y)`
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