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Question
Expand the expression: `(2/x - x/2)^5`
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Solution
By using Binomial Theorem, the expression `(2/x - x/2)^5` can be explained as
`(2/x - x/2)^5 = ^5C_0 (2/x)^5 - ^5C_1 (2/x)^4 (x/2) + ^5C_2 (2/x)^3 (x/2)^2`
- `""^5C_3 (2/x)^2 (x/2)^3 + ^5C_4 (2/x) (x/2)^4 - ^5C_5 (x/2)^5`
= `(32)/x^5 - 5 (16/(x^4)) (x/2) + 10 (8/x^3) (x^2/4) - 10 (4/x^2) (x^3/8) +5 (2/x)(x^4/16) - x^5/32`
= `32/x^5 - 40/x^3 + 20/x - 5x + 5/8 x^3 - x^5/32`
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