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Find middle term in the expansion of ( x/3 + 9y)⁸

D e a r s t u d e n t, {(\frac{x}{3} + 9 y)}^{8} M i d d l e t e r m = \frac{8}{2} + 1 = 5^{t h} t e r m t_{r + 1} = {}^{n}C_{r} {(\frac{x}{3})}^{r} {(9 y)}^{n - r} t_{4 + 1} = t_{5} = {}^{8}C_{4} {(\frac{x}{3})}^{4} {(9 y)}^{10 - 4} = {}^{8}C_{4} {(\frac{x}{3})}^{4} {(9 y)}^{6} {}^{8}C_{4} = \frac{n!}{r! (n - r)!} = \frac{8!}{(8 - 4)! 4!} = \frac{8 \times 7 \times 6 \times 5 \times 4!}{4 \times 3 \times 2 \times 1 \times 4!} = 70 {}^{8}C_{4} {(\frac{x}{3})}^{4} {(9 y)}^{6} = 70 \times \frac{x^{4}}{81} \times 9^{6} \times y^{6} = 459270 x^{4} y^{6} R e g a r d s

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