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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