Question : If $(a+b+c)=20$ and $a^2+b^2+c^2=152$, find the value of $a^3+b^3+c^3-3 abc$.

Option 1: 560

Option 2: 640

Option 3: 480

Option 4: 720

Question : If $(a+b+c)=14$ and $\left(a^3+b^3+c^3-3abc\right)=98$, find the value of $\left(a^2+b^2+c^2\right)$.

Option 1: 70

Option 2: 64

Option 3: 68

Option 4: 72

Question : What is the value of ${a}^3+{b}^3+{c}^3$ if $(a+b+c)=0$?

Option 1: $a^2+b^2+c^2-3abc$

Option 2: $0$

Option 3: $3abc$

Option 4: $a^2+b^2+c^2-ab-bc-ca$

Question : If a + b + c = 0, the value of (a³ + b³ + c³) is:

Option 1: abc

Option 2: 2abc

Option 3: 3abc

Option 4: 0

Question : a³ + b³ + c³ = 3abc if _________.

Option 1: a = b = c

Option 2: a + b + c = 0

Option 3: a + b + c = 1

Option 4: a + b + c = –1