2. The Binomial Theorem states that given any real numbers a and b and any nonnegative integer n,
| (a + b)n | = | n | ( |
n | ) | an-k bk |
| S | ||||||
| k | ||||||
| k=0 |
The coefficient of m2 n8 in the expansion of (m + n)10 will occur when k = 8.
The term in which m2 n8 occurs is C(10,8) m2 n8 and hence the coefficient of m2 n8 is 45.