3. 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 x6 y3 in the expansion of (5x - 3y)9 will occur when k = 3.
The term in which x6 y3 occurs is C(9,3) (5x)6 (-3y)3 and hence the coefficient of x6 y3 is 84 · 56 · (-3)3 = -35437500.