If `2x+3y=13` and `x y=6,` find the value of `8x^3+27 y^3`

Explanation

Given,
`2x+3y=13`
Cubing both sides :
`(2x+3y)^3=(13)^3`
we know
`(a+b)^3=a^3+b^3+3ab(a+b)` ,
`=>` `8x^3+27y^3+3×2x×3y(2x+3y)=2197`
`=>` `8x^3+27y^3+18xx(xy)xx(13)=2197`
`=>` `8x^3+27y^3+18×6×13=2197`
`=>` `8x^3+27y^3+1404=2197`
`=>` `8x^3+27y^3=2197-1404`
`=>` `8x^3+27y^3=793`