Evaluate each of the following: `(10. 4)^3` (ii) `(598)^3` (iii) `(99)^3`

Explanation

Using the identity,

`(a+b)^3 = a^3 + b^3 + 3ab(a+b)`
Given
`(i)=>(10.4)^3=(10+0.4)^3`
`=10^3+0.4^3 +3.10.(0.4)(10+0.4)`
`= 1000+ 0.064 +124.8`
`=1000+124.864`
`=>(10.4)^3=1124.864`
Using the identity,

`(a−b)^3 = a^3 - b^3 -3ab(a-b)`
Given
`(ii)=>(598)^3 = (600 − 2)^3`
`=(598)^3 = 600^3-2^3-3.600.2(600-2)`
`(598)^3 = 216000000-8-2152800`
`=>(598)^3 = 213847192`
Using the identity,
`(a−b)^3 = a^3- b^3 - 3ab(a - b)`
Given
`(iii) => (99)^3 = (100 − 1)^3`
`=> (99)^3 = 100^3 - 1^3 - 3.100.1(100-1)`
`=> (99)^3 = 1000000-1-29700`
`=>(99)^3 = 970299`
Hence the answers are `1124.864 , 213847192 , 970299`