Question

find the middle term of the expansion of (3x+7y)10​

Answer 1

The middle term of the given expansion is 1029193452x⁵y⁵.

Step-by-step explanation:

The given expression is

$(3x+7y)^{10}$

We need to find the middle term of the expansion of given expression.

In the binomial expanding of $(a+b)^n$

$T_{r+1}=^nC_ra^{n-r}b^r$

If n is even, then the middle term is $(\frac{n}{2}+1)th$ term.

In the given expression n=10 which an even number.

$(\frac{n}{2}+1)th=(\frac{10}{2}+1)th=6th$

The 6th term of the expansion is

$T_{5+1}=^(10)C_(5)(3x)^{10-5}(7y)^5$

$T_{6}=(\frac{10!}{5!(10-5)!})(3x)^{5}(7y)^5$

$T_{6}=252(3)^5(7)^5x^5y^5$

$T_{6}=1029193452x^5y^5$

Therefore, the middle term of the given expansion is 1029193452x⁵y⁵.

#Learn more

Middle term of the binomial expansion : https://brainly.in/question/13271941

Answer 2

Answer:

I hope this pic helps you☺️☺️

Step-by-step explanation:

Thank you✌️✌️☺️☺️