Question

Find the coefficient of x¹⁵ in the expansion of (x – x²)¹⁰.

Answer 1

The given expression is (x – x²)¹⁰

General Term `"T"_(r + 1) = ""^n"C"_r ^(n - r) y^r`

= `""^10"C"_r (x)^(10 - r)  (- x^2)r`

= `""^10"C"_r (x)^(10 - r) (-1)^r * (x^2)^r`

= `(-1)^r * ""^10"C"_r (x)^(10 - r + 2r)`

= `(-1)^r * ""^10"C"_r (x)^(10 + r)`

To find the coefficient of x¹⁵

Put 10 + r = 15

⇒ r = 5

∴ Coefficient of x¹⁵ = `(-1)^5  ""^10"C"_5`

= `- ""^10"C"_5`

= – 252

Hence, the required coefficient = – 252