**8/07/2014
**Find
the term in the expansion (3x – 2y)^{5}
that contains x^{2}y^{3}.

**Scroll
down for the solution.**

**8/07/2014
**Solution.

Since,
in general, the *k*th
term of (x + y)^{n}
is ^{n}C_{k
– }_{1}
x^{
(}^{n}^{
– }^{k}^{)}·y^{k},
that for (3x – 2y)^{5}
is

^{5}C_{k}_{
– }_{1}
(3x)^{
(5 – }^{k}^{)}·(-2y)^{k
}so
that with *k
*=
3 – because the exponent of y should be 3 – we have ^{5}C_{3}_{
– }_{1}
(3x)^{
(5 – }^{3}^{)}·(-2y)^{3}
= -720x^{2}y^{3}.^{
}