Answer:
70 is the required coefficient.
Step-by-step explanation:
We have been given [tex](x+y)^8[/tex]
Using the general formula which is:
[tex](x+y)^n=^nC_{0}x^n\cdot y^0+^nC_{1}x^{n-1}y^1+^nC_[2}x^{n-2}y^2+........+^nC_{n}x^0y^n[/tex]
Here, n=8 now, substituting the values in the formula we get:
[tex](x+y)^8=^8C_{0}x^8y^0+^8C_{1}x^7y^1+^8C_{2}x^6y^2+^8C_{3}x^5y^3+^8C_{4}x^4y^4+....[/tex]
So, we want coefficient of[tex]x^4y^4[/tex]
Coefficient is multiple with the term we need to find coefficient of.
[tex]^8C_{4}[/tex] is coefficient of [tex]x^4y^4[/tex]
Using [tex]^nC_{r}=\frac{n!}{r!(n-r)!}[/tex]
[tex]^8C_{4}=\frac{8!}{4!(8-4)!}[/tex]
[tex]\Rightarrow 70[/tex]
