Question

Expand the expression\( (\frac{2}{x} - \frac{x}{2})^5\).

Answer 1

Given:

(2/x − x/2)⁵

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Step 1: Apply Binomial Theorem

(a − b)⁵ = a⁵ − 5a⁴b + 10a³b² − 10a²b³ + 5ab⁴ − b⁵

Let
a = 2/x,   b = x/2

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Step 2: Evaluate each term

a⁵ = 32/x⁵

5a⁴b = 40/x³

10a³b² = 20/x

10a²b³ = 5x

5ab⁴ = 5x³/8

b⁵ = x⁵/32

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Step 3: Write the expansion

(2/x − x/2)⁵ =

32/x⁵ − 40/x³ + 20/x − 5x + 5x³/8 − x⁵/32

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Final Answer:

(2/x − x/2)⁵ = 32/x⁵ − 40/x³ + 20/x − 5x + 5x³/8 − x⁵/32