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

c. 70 if you're on APEX                   

Answer 2

Answer:

The correct option is C.

Step-by-step 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

$^8C_4=\frac{8!}{4!(8-4)!}$

$^8C_4=\frac{8\times 7\times 6\times 5\times 4!}{4!4!}$

$^8C_4=70$

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