Find the seventh term of the expansion

Please select the best answer from the choices provided

A
B
C
D

Question

contestada

Respuesta :

frika frika · Answer 1 · 2019-01-26T22:46:45+01:00

Answer:

Correct choice is A

Step-by-step explanation:

The i-th term of the binomial expansion [tex]\left(-3x-2y\right)^{11}[/tex] is

[tex]T_i=C^{11}_{i-1}\cdot \left(-3x\right)^{11+1-i}\cdot (-2y)^{i-1}.[/tex]

If i=7, then

[tex]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.[/tex]

Note that

[tex]C_6^{11}=\dfrac{11!}{6!(11-6)!}=\dfrac{6!\cdot 7\cdot 8\cdot 9\cdot 10\cdot 11}{6!\cdot 1\cdot 2\cdot 3\cdot 4\cdot 5}=462.[/tex]

alinakincsem alinakincsem · Answer 2 · 2019-01-27T18:10:29+01:00

Answer:

[tex]462 (3x)^5 (7y)^6[/tex]

Step-by-step explanation:

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

[tex](-3x-2y)^{11}[/tex]

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.

[tex]C^{11}_{7-1}=\frac{11!}{6!(11-6)!} = \frac{6!.7.8.9.10.11}{6!.1.2.3.4.5} = 462[/tex]

Therefore, the seventh term of the expansion of [tex](-3x-2y)^{11}[/tex] is [tex]462(-3x)^5(-2y)^6[/tex]