Question

What is the coefficient of the fifth term in (a+b)^9

Answer 1

If you expand this using pascals triangle you will see that the fifth term is 126a^5b^4

the coefficient is the number 126

Answer 2

The coefficient of the fifth term is 126.

Explanation:

The question implies that after the expansion of
`(a+b)^(9)`, what would be the coefficient of the fifth term. This long expansion can be easily done by the application of the Pascal principle of expansion.

Thus,

`(a+b)^(9)` =
`a^(9)` +
`9a^(8)b` +
`36a^(7) b^(2)` +
`84a^(6)b^(3)` +
`126a^(5)b^(4)` +
`126a^(4) b^(5)` +
`84a^(3) b^(6)` +
`36a^(2) b^(7)` +
`9ab^(8)` +
`b^(9)`

So, from this expansion, the fifth term is
`126a^(5)b^(4)`. And its coefficient is 126.