ayhamibrah69
Answered

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coefficient of x^3 in the expansions of
(4+x)^4

Sagot :

Strucid

Answer:

−

344064

x

3

Explanation:

There's a quick way to answering questions like this without the need to go through the whole process of finding the terms before the  

x

3

term:

Using the  

n

C

r

button, the value of  

n

represents the expansion power of  

9

and the  

r

would be the term you want to find, so in this case, it would be  

3

.

Therefore, the coefficient of the general  

x

3

term is:

9

C

3

=

84

However, you can only do this if the expansion is in the format of  

(

1

+

x

)

n

.

To find the  

x

3

coefficient for  

(

4

−

x

)

9

:

(

a

+

x

)

n

=

a

n

+

n

a

n

−

1

x

+

(

n

(

n

−

1

)

2

!

)

a

n

−

2

x

2

+

(

n

(

n

−

1

)

(

n

−

2

)

3

!

)

a

n

−

3

x

3

+

...

...

+

x

n

Step-by-step explanation:

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