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15 votes
Coefficient of x^3 in the expansions of
(4+x)^4

1 Answer

10 votes

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

Explanation:

User Lgabster
by
3.2k points