Question

I. Find coefficient of x^6y^3 in the expansion of (x + 2y)^9.​

Answer 1

Answer:

The coefficient of x⁶y³ is 4032.

Step-by-step explanation:

The kth term of a binomial expansion (a + b)ⁿ is:

$n^{th}\ term=\frac{n!}{(n-(k-1))!}a^{(n-(k-1))}b^{(k-1)}$

The binomial term is (x + 2y)⁹.

The term for which the coefficient is to be found is x⁶y³.

Consider x⁶:

$a^{(n-(k-1))}=x^{6}\\n-(k-1)=6\\9-(k-1)=6\\k-1=3\\k=4$

That is we need to determine the 4th term.

$4^{th}\ term=\frac{9!}{(9-(4-1))!}(x)^{(9-(4-1))}(2y)^{(4-1)}\\=504\times x^{6}\times 8y^{3}\\=4032x^{6}y^{3}$

Thus, the coefficient of x⁶y³ is 4032.