If (a + 4)3 = a3 + 12a2 + ka +...

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If (a + 4)³ = a³ + 12a² + ka + 64, then what is the value of k?

A. 45

B. 46

C. 47

D. 48

Answer: Option D

Solution (By Examveda Team)

(a + b)³ = a³ + 3a²b + 3ab² + b³ . . . . . . . . (i)
(a + 4)³ = a³ + 12a² + ka + 64
= (a)³ + 3.a².4 + k.a + (4)³ . . . . . . . . (ii)
Comparing equation (i) and (ii) we get,
b = 4 and k = 3k²
∴ k = 3 × 4² = 48

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If (a + 4)3 = a3 + 12a2 + ka +...

If (a + 4)3 = a3 + 12a2 + ka + 64, then what is the value of k?

Solution (By Examveda Team)

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If (a + 4)³ = a³ + 12a² + ka + 64, then what is the value of k?