Question

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

Answer 1

Given:

There are given the expression:

$(x-10y)^7$

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,

$(x-10y)^7=\frac{7!}{0!(7-0)!}x^7(-10y)^0+\frac{7!}{1!(7-1)!}x^6(-10y)^1+\frac{7!}{2!(7-2)!}x^5(-10y)^2+\frac{7!}{3!(7-3)!}x^4(-10y)^3$

Then,

$\begin{gathered} (x-10y)^{7}=\frac{7!}{0!(7-0)!}x^{7}(-10y)^{0}+\frac{7!}{1!(7-1)!}x^{6}(-10y)^{1}+\frac{7!}{2!(7-2)!}x^{5}(-10y)^{2}+\frac{7!}{3!(7-3)!}x^{4}(-10y)^{3} \\ (x-10y)^7=x^7-70x^6y+2100x^5y^2-35000x^4y^3 \end{gathered}$

So,

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

$-35000x^4y^3$

Final answer:

Hence, the correct option is B.