Which of the following is correct:

Question

Which of the following is correct:

1. A. (a − b)(a + b) = a² − b² (Correct answer)
2. B. (a + b)² = a² + b² − 2ab
3. C. (a + b)³ = a³ + b³
4. D. (a − b)² = a² + b² + 2ab

Correct Answer

Option A — (a − b)(a + b) = a² − b²

Detailed Solution & Explanation

The correct answer is (a − b)(a + b) = a² − b².

Key Points

• (a − b)(a + b) = a² − b² is the standard difference-of-squares identity and is correct.
• The others are all misstated:
  • (a + b)² = a² + b² + 2ab, not −2ab
  • (a + b)³ = a³ + b³ + 3ab(a + b), not a³ + b³
  • (a − b)² = a² + b² − 2ab, not +2ab

Additional Information

• The identities most often tested: a³ + b³ = (a + b)(a² − ab + b²) and a³ − b³ = (a − b)(a² + ab + b²).
• Also worth memorising: (a + b + c)² = a² + b² + c² + 2(ab + bc + ca).
• The difference of squares is a fast mental-arithmetic tool: 43 × 37 = (40 + 3)(40 − 3) = 1600 − 9 = 1591.