Answer:
The correct option is C.
Step-by-step explanation:
The given expression is
[tex](x+y)^8[/tex]
Use binomial expansion to find the coefficients of [tex]x^4y^4[/tex].
[tex](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}[/tex]
[tex](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[/tex]
Therefore coefficients of [tex]x^4y^4[/tex] is
[tex]^8C_4=\frac{8!}{4!(8-4)!}[/tex]
[tex]^8C_4=\frac{8\times 7\times 6\times 5\times 4!}{4!4!}[/tex]
[tex]^8C_4=70[/tex]
Therefore the coefficients of [tex]x^4y^4[/tex] is 70 and option C is correct.
