Question:
Find the 8th term in the expansion of $\left(x^{3 / 2} y^{1 / 2}-x^{1 / 2} y^{3 / 2}\right)^{10} .$
Solution:
We need to find the 8th term in the given expression.
$\because T_{8}=T_{7+1}$
$\therefore T_{8}={ }^{10} C_{7}\left(x^{3 / 2} y^{1 / 2}\right)^{10-7}\left(-x^{1 / 2} y^{3 / 2}\right)^{7}$
$=-\frac{10 \times 9 \times 8}{3 \times 2} x^{9 / 2} y^{3 / 2}\left(x^{7 / 2} y^{21 / 2}\right.$)
$=-120 x^{8} y^{12}$