Factorise : `(i) 125a^(3)+(1)/(8) " " (ii) 8a^(3)-27b^(3)`

Explanation

`(i) 125a^(3)+(1)/(8)=(5a)^(3)+((1)/(2))^(3)`
`=x^(3)+y^(3) " " ("where" x=5a " and" y=(1)/(2))`
`=(x+y)(x^(2)+y^(2))`
`=(5a+(1)/(2))(25a^(2)-(5)/(2)a+(1)/(4))`
`(ii) 8a^(3)-27b^(3)=(2a)^(3)-(3b)^(3)`
`=x^(3)-y^(3) " " ("where" x=2a " and" y=3b)`
`=(x-y)(x^(2)+xy+y^(2))`
`=(2a-3b)(4a^(2)+6ab+9b^(2))`