If a + b + c = 6 and $ a^2 + b^2 + c^2 = 40 , $ then what is the value of $a^3 + b^3 + c^3 -3abc ?$

252

a³ + b³ = ( a + b ) ( a² + b² - ab )

( a + b )² = a² + b² + 2ab

If a + b + c = 6

$ a^2 + b^2 + c^2 = 40 , $ 

what is the value of $a^3 + b^3 + c^3 -3abc $?

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 c = 0

If a + b = 6

$ a^2 + b^2 = 40 , $ 

( 6 )² = 40 + 2ab

36 - 40 = 2ab

ab = -2

what is the value of $a^3 + b^3 $ =  ( a + b ) ( a² + b² - ab )

= $a^3 + b^3 $ =  ( 6 ) ( 40 - (-2) )

$a^3 + b^3 $  = 252