Solveeit Logo
Login

Question

Mathematics Question on Binomial theorem

The term independent of xx in the expansion of (x−3x2)18(x- \frac {3} {x^2})^{18}

A

18C6^{18}C_6

B

18C6 36^{18}C_6 \, 3^6

C

18C12 3−6^{18}C_{12} \, {3}^{-6}

D

363^6

Answer

18C6 36^{18}C_6 \, 3^6

Explanation

Solution

Tr+1= 18crx18−r(−3x2)rT_{r+1} = \,^{18}c_{r}x^{18-r} \left(-\frac{3}{x^{2}}\right)^{r} = 18crx18−r−2r(−3)r= \, ^{18}c_{r}x^{18-r-2r}\left(-3\right)^{r} ∴18−3r=0\therefore 18 - 3r = 0 ⇒r=6\Rightarrow r = 6 ∴\therefore reqd. term = 18c6(−3)6= 18c6(3)6=\, ^{18}c_{6}\left(-3\right)^{6} = \, ^{18}c_{6}\left(3\right)^{6}.