Question

What is the coefficient of x^4y^4 in the expansion of (x + y)^8?

A. 1
B. 4
C. 70
D. It does not exist.

Answer 1

The correct option is C.

Explanation:

The given expression is

`(x+y)^8`

Use binomial expansion to find the coefficients of
`x^4y^4`.

`(x+y)^8=^8C_0x^0y^(8-0)+^8C_1x^1y^(8-1)+^8C_2x^2y^(8-2)+^8C_3x^3y^(8-3)+^8C_4x^4y^(8-4)+^8C_5x^5y^(8-5)+^8C_6x^6y^(8-6)+^8C_7x^7y^(8-7)+^8C_8x^8y^(8-8)`

`(x+y)^8=^8C_0x^0y^8+^8C_1x^1y^7+^8C_2x^2y^3+^8C_3x^3y^5+^8C_4x^4y^4+^8C_5x^5y^3+^8C_6x^6y^2+^8C_7x^7y+^8C_8x^8y^0`

Therefore coefficients of
`x^4y^4` is

`^8C_4=(8!)/(4!(8-4)!)`

`^8C_4=(8* 7* 6* 5* 4!)/(4!4!)`

`^8C_4=70`

Therefore the coefficients of
`x^4y^4` is 70 and option C is correct.