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
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Correct Answer: a 3 –12a 2 + 48a – 64
Solution : We know that, (a – b) 3 = a 3 – 3a 2 b + 3ab 2 – b 3 So, (a – 4) 3 = a 3 – 3a 2 × 4 + 3a × (4) 2 – (4) 3 ⇒ (a – 4) 3 = a 3 – 12a 2 + 48a – 64 Hence, the correct answer is 'a 3 – 12a 2 + 48a – 64'.
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