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Question
Find the constant term of `(2x^3 - 1/(3x^2))^5`
Solution
General term Tr+1 = `""^5"C"_"r" (2x^3)^(5 - "r") ((-1)/(3x^2))^"r"`
= `""^5"C"_"r" 2^(5 - "r") x^(15 - 3"r") (- 1)^"r" 1/(3^"r") 1/(x^(2"r"))`
= `""^15"C"_"r" (2^(5 - "r"))/(3^"r") (- 1)^"r" x^(15 - 3"r" - 2"r")`
= `""^5"C"_"r" (- 1)^"r" (2^(5 - "r"))/(3^"r") x^(15 - 5"r")`
To find the constant term
15 – 5r = 0
⇒ 5r = 15
⇒ r = 3
∴ Constant term = `""^5"C"_3 (- 1)^3 (2^(5 - 3))/3^3`
= `(5 xx 4 xx 3)/(3 xx 2 xx 1) (- 1) ((2^2))/3^3`
= `(10 - (- 1)(4))/27`
= `(- 40)/27`
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