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