Question

coefficient of x^2 y^3y^4 in the form (x+y+z)^n is A find the coefficient of x^4 y^4 z​

Answer 1

Step-by-step explanation:

(x+y+z)

4

=

4

C

0

x

0

(y+z)

4

+

4

C

1

x(y+z)

3

+

4

C

2

x

2

(y+z)

2

+

4

C

3

x

3

(y+z)+

4

C

4

x

4

(y+z)

3

We are intended in term 4C

2

x

2

(y+z)

2

4

C

2

x

2

(y+z)

2

=

2

4×3

x

2

(y

2

+z

2

+2yz)

=6x

2

y

2

+6x

2

z

2

+

12x

2

yz

coefficient of x

2

yz→12