Factorise
(i) `1+64x^(3)`(ii) `a^(3)-2sqrt(2)b^(3)`

Explanation

(i) `1+64x^(3)=(1)^(3)+(4x)^(3)`
` =(1+4x)[(1)^(2)-(1)(4x)+(4x)^(2)]`
[using ieentity,`a^(3)-b^(3)=(a+b)(a^(2)-ab+b^(2))`]
` =(1+4x)(1-4x+16x^(2))`
(ii) ` a^(3)-2sqrt(2)b^(3)=(a)^(3)-(sqrt(2)b^(3)=(a)^(3)-(sqrt(2)b)^(3)`
`=(a-sqrt(2)b)[a^(2)+a(sqrt(2b))+(sqrt(2)b)+(sqrt(2)b)^(2)]`
[using identity,`a^(3)-b^(3)=(a-b)(a^(2)+ab+b^(2)`]
` =(a-sqrt(2)b)(a^(2)+sqrt(2)ab+ab^(2))`