Factroise
`(i) 1+64x^3`
`(ii) 27x^3+125y^3`
`(iii) (x+1)^3+(x-1)^3`

Explanation

We have
`(i) 1+64x^3`
`=(1)^3+(4x)^3`
`=(1+4x)(1-4x+16x^2)`
`(ii) 27x^3+125y^3`
`=(3x)^3+(5y)^3`
`=(3x+5y)(9x^2-15xy+25y^2)`
(iii) Putting `(x+1)=a and (x-1)=b`, we get
`(x+1)^3+(x-1)^3`
`=(a^3+b^3)`
` =(a+b)(a^2-ab+b^2)`
` ={(x+1)+(x-1)}xx {(x+1)^2-(x+1)(x-1)+(x-1)^2}`
` =2xxx{(x^2+2x+1)-(x^2-1)+(x^2-2x+1)}`
` =2xx(x^2+2x+1-x^2+1+x^2-2x+1)=2x(x^2+3)`.