Simplify (x^(5/2)+y^(5/2))(x^(5/2)-y^(5/2))

Problem

(x(5/2)+y(5/2))*(x(5/2)−y(5/2))

Solution

1. Identify the pattern as a difference of squares, which follows the algebraic identity (a+b)*(a−b)=a2−b2

2. Substitute the terms into the identity where a=x(5/2) and b=y(5/2)

3. Apply the power of a power rule, (xm)n=x(m⋅n) to each term.

4. Simplify the exponents by multiplying 5/2⋅2=5

Final Answer

(x(5/2)+y(5/2))*(x(5/2)−y(5/2))=x5−y5

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