Question

Find the 4th term in the expansion of (x - 10y)^7

Answer 1

Given:

There are given the expression:

`(x-10y)^7`

Step-by-step explanation:

According to the question:

We need to find the 4th term in the expansion.

So,

From the given expression:

`(x-10y)^(7)`

To find the 4th expansion, we will use the binomial theorem:

So,

From the binomial expansion:

`(a+b)^n=\sum_{i\mathop{=}0}^n(n,i)a^(n-i)b^i`

Then,

Use the above formula in the given expression:

So,

From the given expression:

`(x-10y)^7=\sum_{i\mathop{=}0}^n(7,i)x^(7-i)(-10y)^i`

Then,

`(x-10y)^7=(7!)/(0!(7-0)!)x^7(-10y)^0+(7!)/(1!(7-1)!)x^6(-10y)^1+(7!)/(2!(7-2)!)x^5(-10y)^2+(7!)/(3!(7-3)!)x^4(-10y)^3`

Then,

So,

The 4th term of the given expansion is shown below:

`-35000x^4y^3`

Final answer:

Hence, the correct option is B.