Question

Find the coefficient of x6y8 in the
in the expansion (4x+y/2)^14​

Answer 1

Given :  (4x + y/2)¹⁴

To Find : the coefficient  of  x⁶y⁸

Solution:

(a + b)ⁿ

r +1 th term is given by

${^n}C_ra^{n-r}b^r$

(4x + y/2)¹⁴

a = 4x

b = y/2

n = 14

x⁶y⁸

=> r = 8

9th term is

¹⁴C₈(4x)⁶(y/2)⁸

4⁶ = 2¹²

= ¹⁴C₈2⁴x⁶y⁸

¹⁴C₈ = 3003

= 3003 * 16 x⁶y⁸

= 48,048 x⁶y⁸

coefficient of  x⁶y⁸  is 48,048

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