Factroise
`(i) a^3-2sqrt(2)b^3`
`(ii)1-64a^3`
`(iii) 8a^3-27b^3`

Explanation

We have
`(i) (a^3-2sqrt(2)b^3)`
`=(a)^3-(sqrt(2)b)^3`
`=(a-sqrt(2)b)xx{a^2+(axx sqrt(2)b)+(sqrt(2)b)^2}`
` =(a-sqrt(2)b(a^2+sqrt(2)ab+2b^2)`
`therefore (a^3-2sqrt(2)b^3)=(a-sqrt(2)b)(a^2+sqrt(2)ab 2b^2)`.
`(ii) (1-64a^3)`
`=(1)^3-(4a)^3`
`=(1-4a)xx{1^2+(1xx4a)+(4a)^2} " " [because x^3-y^3=(x-y)(x^2+xy+y^2)]`
`=(1-4a)(1+4a+16a^2)`
`therefore (1-64a^3)=(1-4a)(1+4a+16a^2)`
`(iii) (8a^3-27b^3)`
`=(2a)^3-(3b)^3`
`=(2a-3b)xx(4a^2+6ab+9b^2)`
`therefore (8a^3-27b^3)=(2a-3b)(4a^2+6ab+9b^2)`.