Question

Find the seventh term of the expansion

Please select the best answer from the choices provided

A
B
C
D

Answer 1

`462 (3x)^5 (7y)^6`

Explanation:

We are given the following expression to be expanded and we are to find its seventh term:

`(-3x-2y)^(11)`

The coefficient here is taken from Pascal's triangle (nCr on the calculator).

For the expansion, the power of the first term decreases by one each time while it increases for the latter term.

`C^(11)_(7-1)=(11!)/(6!(11-6)!) = (6!.7.8.9.10.11)/(6!.1.2.3.4.5) = 462`

Therefore, the seventh term of the expansion of
`(-3x-2y)^(11)` is
`462(-3x)^5(-2y)^6`

Answer 2

Correct choice is A

Explanation:

The i-th term of the binomial expansion
`\left(-3x-2y\right)^(11)` is

`T_i=C^(11)_(i-1)\cdot \left(-3x\right)^(11+1-i)\cdot (-2y)^(i-1).`

If i=7, then

`T_7=C^(11)_(7-1)\cdot \left(-3x\right)^(11+1-7)\cdot (-2y)^(7-1)=C^(11)_6\cdot (-3x)^5\cdot (-2y)^6=462\cdot (-3x)^5\cdot (-2y)^6.`

Note that

`C_6^(11)=(11!)/(6!(11-6)!)=(6!\cdot 7\cdot 8\cdot 9\cdot 10\cdot 11)/(6!\cdot 1\cdot 2\cdot 3\cdot 4\cdot 5)=462.`