Question

What is the coefficient of x 101 y 99 in the expansion of (2x 3y) 200?

Answer 1

Answer:

²⁰⁰C₉₉* 2¹⁰¹ * 3⁹⁹

or

-²⁰⁰C₉₉* 2¹⁰¹ * 3⁹⁹

Step-by-step explanation:

the coefficient of x¹⁰¹ y ⁹⁹ in the expansion of (2x + 3y) ²⁰⁰  or (2x - 3y) ²⁰⁰

Using

(a + b)ⁿ = aⁿ + (ⁿC₁)aⁿ⁻¹b + (ⁿC₂)aⁿ⁻²b² + … + (ⁿCₙ₋₁)abⁿ⁻¹ + bⁿ

Here a = 2x     & b = 3y  or - 3y

x¹⁰¹ = x²⁰⁰⁻⁹⁹

²⁰⁰C₉₉ (2x)²⁰⁰⁻⁹⁹ (3y)⁹⁹       or ²⁰⁰C₉₉ (2x)²⁰⁰⁻⁹⁹ (-3y)⁹⁹

Coefficient

= ²⁰⁰C₉₉* 2¹⁰¹ * 3⁹⁹            or  -²⁰⁰C₉₉* 2¹⁰¹ * 3⁹⁹