If x + y + z = 8, and x^2 + y^2 + z^2 = 20 then the value of x^3 + y^…

If x + y + z = 8, and $x^2 + y^2 + z^2 = 20$

Find the value of $x^3 + y^3 + z^3 − 3xyz$

If the number of equations are less than the number of variables then we can put the extra variables according to our choice = 

So here two equations given and three variables are present so put z = 0

x + y = 8, and $x^2 + y^2  = 20$

Find the value of $x^3 + y^3$= ?

( a + b )² = a² + b² + 2ab

( 8)² = 20 + 2xy

64 =  20 + 2ab

2xy = 44

xy = 22

$x^3 + y^3$ = 8³ - 3 × 8 × 22

$x^3 + y^3$ = 512 - 528

$x^3 + y^3$ = -16