Answer:
-26730
Explanation:
To find the coefficient of [tex]x^7[/tex] in the expansion of [tex](3 -x)^{11}[/tex]
Use Binomial Expansion:
[tex](x+y)^n = \ ^n C_0 x^n + \ ^n C_1 x^{n-1} y + \ ^n C_2 x^{n-2}y^2 + ...+ \ ^n C_n y^n[/tex]
In this expansion,
[tex](3-x)^{11}[/tex]
The coefficient of [tex]x^7[/tex]
[tex]= 11C_{7} (3)^{11-7} (-x)^7[/tex]
[tex]= (330) (81) (-x^7)[/tex]
[tex]= -26730x^7[/tex]
