Question

Write the middle term in the expansion of (2x + 5y)6​

Answer 1

Answer:

Since n is even number, (

2

8

+1)

th

term i.e., 5th term is the middle term in (2x + 3y)

8

.

T

5

=T

4+1

=

8

C

4

(2x)

8−4

(3y)

4

=

8

C

4

(2x)

4

(3x)

4

Answer 2

The middle term of expansion of $(2x+5y)^{6}$ is 20000$x^{3} y^{3}$.

Given:

$(2x+5y)^{6}$

To find:

Middle terms = ?

Formula to be used:

General term in binomial expansion = $T_{r+!} = C_{r} ^{n} a^{n-r} b^{n}$

Middle term of series if n is even = $[\frac{n}{2} +1]$th term.

Using formula,

middle term of $(2x+5y)^{6}$ is 4th term

r = 4

From the given polynomial, a = 2x and b = 5y.

$T_{4} = C_{3}^{6} (2x)^{3} (5y)^{3}\\ \\T_{4} = 20000x^{3} y^{3}$

Therefore. the middle term of expansion of $(2x+5y)^{6}$ is 20000$x^{3} y^{3}$.