Evaluate each of the following: (i)`111^3-\ 89^3` (ii) `46^3+34^3`

Explanation

Using Identity,

`(a−b)^3=a^3−b^3−3ab(a−b)`
Given,
`(i)111^3−89^3`
`=>(111−89)^3 =111^3 −89^3−3(111)(89)(111−89)`
`=>10648=111^3−89^3−652014`
`:.111^3−89^3=662662`
Given,
`(ii)46^3 +34^3`
Then,
`46^3 +34^3`
Can be written as
`=>
(50−4)^3+(40−6)^3`
`=>50^3−4^3−3 xx 50 xx 4(50−4)+40^3−6^3−3 xx 40 xx 6(40−6)`
`=>625000−64−30000+2400+64000−216−28800+4320`
`=>636640`
Hence, answers are obtained.