If `a+b=10` and `a^2+b^2=58` , find the value of `a^3+b^3`

Explanation

Given
`a+b=10`
we know
`(a+b)^2=a^2+b^2+2ab`
`10^2=58+2ab`
`2ab=100−58=42`
`ab=21`
`(a+b)^3=a^3+b^3+3ab(a+b)`
`10^3=a^3+b^3+3×21×10`
`a^3+b^3=1000−630=370`