Question

Find the coefficient of x^5y^7 in the expansion of (x-2y)^12

Answer 1

Answer:

-1584

Step-by-step explanation:

For the expansion of (x-2y)^12

General Term(G.T) = 12Cr × x^(12-r)(-2y)^r

∴For the term X^5 y^7

y=7

∴r=7

8th term = 12C7 × x^(12-7) (-2y)^7

              =12C7×(-2^7) × x^5 y^7

              =-1584 x^5 y^7

Answer 2

Concept

Binomial theorem

Expansion of  $(a+b)^{n}$ is$n C_{0} a^{n} \cdot b^{0}+n C_{1} a^{n-1} \cdot b^{1}+n C_{2} a^{n-2} \cdot b^{2}+\ldots \ldots \ldots+n C_{n} a^{n-n} \cdot b^{n}\end{aligned}$

Where $n C_{r}=\frac{n !}{r ! \cdot(n-r) !}$

Given

The expansion $(x-2y)^{12}$.

Find

We have to find the coefficient of $x^5y^7$.

Solution

By evaluating with general expansion.

Here a= x , b= -2y , n= 12

$x^5y^7$will be in the 8th term.

Then

$T_8&=12C_7\times x^{(12-7)} (-2y)^7$

   $=12C_7\times (-2^7) \times x^5 y^7$

   $=-1584 x^5 y^7$

Hence the coefficient is -1584.