Question : If $9 a+9 b+9 c=81$ and $4 a b+4 b c+4 c a=160$, then what is the value of $6 a^2+6 b^2+6 c^2$?

Option 1: 1

Option 2: 3

Option 3: 4

Option 4: 6

Question : If $(a+b+c) \neq 0$, then $(a+b+c)\left(a^2+b^2+c^2-a b-b c-c a\right)$ is equal to:

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

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

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

Option 4: $a^3+b^3+c^3+3abc$

Question : If $a+b+c=0$ and $a^2+b^2+c^2=40$, then what is the value of $a b+b c+c a$?

Option 1: –30

Option 2: –20

Option 3: –25

Option 4: –40

Question : If $a + b + c = 12$ and $ab + bc + ca = 22$, then what is the value of $a^3 + b^3 + c^3 - 3abc ?$

Option 1: 1052

Option 2: 936

Option 3: 924

Option 4: 876

Question : What is the value of (a + b + c) {(a - b)² + (b - c)² + (c - a)²}?

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

Option 2: $2a^3+2b^3+2c^3-6abc$

Option 3: $3abc$

Option 4: $6abc$