Question : What is the value of $(a-b)^3 - a^3 + b^3$?

Option 1: $3ab(a-b)$

Option 2: $-3ab(a+b)$

Option 3: $3ab(a+b)$

Option 4: $-3ab(a-b)$

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 : 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 : What is the expansion of (a - 4)³?

Option 1: a³ – 12a² + 48a + 64

Option 2: a³ + 12a² + 48a + 64

Option 3: a³ –12a² + 48a – 64

Option 4: a³ +12a² + 48a – 64

Question : If a + b + c = 15 and a² + b² + c² = 83 then the value of a³ + b³ + c³ – 3abc:

Option 1: 200

Option 2: 180

Option 3: 190

Option 4: 210