Respuesta :
use the binomial expansion formula for (a+b)^n
(sorry, cannot type it here, please google)
n!/[(n-k)!k!]a^(n-k)b^k
x^6y^3 is when k=3
in this case, n=9
so the coefficient when k=3 is: 9!/[(9-3)!3!]*(2)^3= [tex] \frac{9*8*7}{3*2*1} *2^3=672[/tex]
(sorry, cannot type it here, please google)
n!/[(n-k)!k!]a^(n-k)b^k
x^6y^3 is when k=3
in this case, n=9
so the coefficient when k=3 is: 9!/[(9-3)!3!]*(2)^3= [tex] \frac{9*8*7}{3*2*1} *2^3=672[/tex]
Answer:
The coefficient of [tex]x^6y^3[/tex] is 672.
Step-by-step explanation:
By the binomial expansion,
[tex](a+b)^n=\sum_{r=0}^n ^nC_r a^{n-r} b^r[/tex]
Where,
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
Thus,
[tex](x+2y)^9=\sum_{r=0}^n ^9C_r x^{9-r} (2y)^r[/tex]
For finding the coefficient of the [tex]x^6y^3[/tex]
r = 3,
Hence, the term in which [tex]x^6y^3[/tex] is present is,
[tex]^9C_3 x^6 (2y)^3[/tex]
[tex]=84\times x^6\times 8y^3[/tex]
[tex]=672x^6y^3[/tex]
Therefore, the coefficient of [tex]x^6y^3[/tex] is 672.
