Question

What is the 8th term of the binomial expansion (x + y) ^10?
Select the correct answer.
A. 120x^7y^3
B. 720x^7y^3
C. 720x^3y^7
D. 120 x^3y^7

Answer 1

Answer:

It is Option D. 120 x^3 y^7

Answer 2

Option D is correct i.e. the eighth term of the given expansion is $120x^{3} y^{7}$.

What is binomial theorem?

The Binomial Theorem is the method of expanding an expression that has been raised to any finite power.

Binomial expression

A binomial expression is an algebraic expression that contains two dissimilar terms .

Formula for finding the general term in binomial expansion

$T_{r+1} =nC_{r} x^{n-r} y^{r}$

According to the given question

We have,

The binomial expansion $(x+y)^{10}$

Therefore,

The eighth term of the given binomial expansion is given by

$T_{7+1} = 10C_7x^{10-7} y^{7} \\T_{8} = \frac{10!}{7!3!} x^{3} y^{7}$

$T_{8} = \frac{(10)(9)(8)(7!)}{7!(3)(2)(1)} x^{3} y^{7}$

$T_{8} = 120x^{3} y^{7}$

Hence, option D is correct. i.e. the eighth term of the given expansion is $120x^{3}y^{7}$.

Learn more about the binomial expansion here:

https://brainly.com/question/12249986

#SPJ2