Question

find the middle term in the expansion 2 by 3 x minus 3 by 2 y whole power 20

Answer 1

given (2x/3 + 3y/2)²⁰
n = 20 ⇒ even
For even Values of n , middle term is (n/2 + 1)th
e.g., middle term = (20/2 + 1)th = 11th
Now, use the formula,
$\bold{T_{r+1}} = ^nC_r(a)^{n-r}b^r$
Here, r = 10, a = 2x/3 and b = 3y/2

Now, T₁₁ = ²⁰C₁₀ (2x/3)²⁰⁻¹⁰ (3y/2)¹⁰
T₁₁ = ²⁰C₁₀(2x/3)¹⁰(3y/2)¹⁰ =²⁰C₁₀ (xy)¹⁰

Answer 2

Answer:

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