Factorize: (i)`x^4-y^4`
(ii) `16 x^4-81`
(iii)`x^4-(y+z)^4`
(iv) `2x-32 x^5`
(v)`3a^4-48 b^4`
(vi) `81 x^4-121 x^2`

Explanation

(i)`x^4-y^4`
`= (x^2)^2-(y^2)^2`
`= (x^2-y^2)(x^2+y^2)`
`= (x-y)(x+y)(x^2+y^2)`
`= (x-y)(x+y)(x^2+y^2)`

(ii) `16 x^4-81`
`= (4x^2)^2-(9)^2`
`=(2x)^2-(3)^2`
`=(2x+3)(2x-3)`

(iii)`x^4-(y+z)^4`
`=(x^2)^2 −{(y+z)^2 }^2 `
`=(x^2 +(y+z) 2 )(x^2 −(y+z)^2)`
`=(x^2 +(y+z) 2 )(x+y+z)(x−y−z)`
`=(x^2 +y^2 +z^2+2yz)(x+y+z)(x−y−z)`
`=1×(x^2+y^2 +z^2+2yz)×(x+y+z)×(x−y−z)`

(iv) `2x-32 x^5`
`=2x(1−16x^4)`
`=2x(1−4x^2)(1+4x^2)`
`=2x(1+4x^2 )(1−2x)(1+2x)`

(v)`3a^4-48 b^4`
`=3a^4-48b^4`
`=3(a^4-16b^4)`
`=3{(a^2+4b^2)(a^2-4b^2)}`
`=3{(a^2+4b^2)(a+2b)(a-2b)}`

(vi) `81 x^4-121 x^2`
`=x^2 (81x^2 −121)`
`=x^2 ((9x)^2 −(11)^2)`
`=x^2 (9x+11)(9x−11)`