Problem

a^{5}(b-c)+b^{5}(c-a)+c^{5}(a-b)

Answer

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Answer

Therefore, the final result is a5(b−c)+b5(c−a)+c5(a−b)

Steps

Step 1 ：Given expression is a5(b−c)+b5(c−a)+c5(a−b)

Step 2 ：Rearrange the terms to group similar terms together, we get a5b−a5c+b5c−b5a+c5a−c5b

Step 3 ：Factor out common terms, we get a5(b−c)+b5(c−a)+c5(a−b)

Step 4 ：This is the simplest form of the expression, so we can't simplify it further

Step 5 ：Check the result, substitute arbitrary values for a, b, and c into the original expression and the final result, they should be equal

Step 6 ：Therefore, the final result is a5(b−c)+b5(c−a)+c5(a−b)

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