Which of the following expression results in zero?
2018
Which of the following expression results in zero?
- A.
(0 + 0 + 1)(0 + 0 + 1)
- B.
(0 + 0 + 0)(0 + 1 + 1)
- C.
(1 + 0 + 0)(1 + 1 + 1)
- D.
(0 + 1 + 0)(1 + 0 + 1)
Attempted by 408 students.
Show answer & explanation
Correct answer: B
Key idea: If any factor in a product is zero, the whole product is zero.
(0 + 0 + 1)(0 + 0 + 1) → 0 + 0 + 1 = 1, 0 + 0 + 1 = 1, so 1 × 1 = 1 (not zero).
(0 + 0 + 0)(0 + 1 + 1) → 0 + 0 + 0 = 0, 0 + 1 + 1 = 2, so 0 × 2 = 0 (zero because one factor is zero).
(1 + 0 + 0)(1 + 1 + 1) → 1 + 0 + 0 = 1, 1 + 1 + 1 = 3, so 1 × 3 = 3 (not zero).
(0 + 1 + 0)(1 + 0 + 1) → 0 + 1 + 0 = 1, 1 + 0 + 1 = 2, so 1 × 2 = 2 (not zero).
Therefore, the expression (0 + 0 + 0)(0 + 1 + 1) results in zero because its first factor equals zero.