How do I find the coefficient of a^4b^8 in the expansion of (a + b)^12?

Question

How do I find the coefficient of a^4b^8 in the expansion of (a + b)^12?

Answer 1

Well you know that the term with a^4b^8 in it is the ninth term because the first term starts with a^12 and works its way down, as the b part does just the opposite. The way you find the coefficient is using combinations. Since the exponent is 12, you will use the number 12. You're going to be finding the coefficient for the ninth term, so you will use the combination 12C8, since 12C0 is the first combination.

So, the answer is 12C8, or 495

Answer 2

terms are

12C0 • a^12 • b^0

12C1 • a^11 • b^1

12C2 • a^10 • b^2

.........

b exponent matches 2nd number on the binomial coefficient, so

12C8 • a^4 • b^8

and 12C8 = 12C4 = (12•11•10•9)/(1•2•3•4) = 55•9 = 495