Question : If a + b + c = 0, then the value of (a + b – c)² + ( b + c – a)² + ( c + a – b)² is:

Option 1: 0

Option 2: 8abc

Option 3: 4(a² + b² + c²)

Option 4: 4(ab + bc + ca)

Question : If a + b + c = 1, ab + bc + ca = –1, and abc = –1, then what is the value of a³ + b³ + c³?

Option 1: 1

Option 2: 5

Option 3: 3

Option 4: 2

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: $6abc$

Question : What is the value of (a + b)³ – a³ – b³?

Option 1: – 3ab(a – b)

Option 2: 3ab(a + b)

Option 3: – 3ab(a + b)

Option 4: 3ab(a – b)

Question : If A + B = – 5 and AB = 6, then find the value of A³ + B³.

Option 1: 35

Option 2: 45

Option 3: –35

Option 4: 215