Binomial Theorem Question 6
Question 6 - 25 January - Shift 1
The constant term in the expansion of
$(2 x+\frac{1}{x^{7}}+3 x^{2})^{5}$ is
Show Answer
Answer: 1080
Solution:
Formula: Multinomial Theorem (ii)
General term is $\sum \frac{5 !(2 x)^{n_1}(x^{-7})^{n_2}(3 x^{2})^{n_3}}{n_1 ! n_2 ! n_3 !}$
For constant term,
$n_1+2 n_3=7 n_2$
$n_1+n_2+n_3=5$
Only possibility $n_1=1, n_2=1, n_3=3$
$\Rightarrow$ constant term $=1080$
