Question

find the 7th term in the expansion of ${(4x-\frac{1}{2\sqrt{x}})}^{13}$

• A. $439296x^7$
• B. $439296x^4$
• C. $439396x^7$
• D. $43396x^4$

Answer 1

Answer: (B)

$439296x^4$

The 7th term of the given binomial expansion will be,
$=$ ${}_6^{13}\text{C}\left(4x{)}^7\right(-\frac{1}{2x^{\frac{1}{2}}}{)}^6$
$=$ $\frac{13!\times 2^{14}\times x^7}{7!.6!\times 2^6.x^3}$
$=$ $\frac{13!\times 2^{14}}{7!\times 6!\times 2^6}{x}^4$
$=439296x^4$