# Proof without using commutative axioms

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How would the following proof be detailed if the commutative axioms did not exist? Explain your answer.

Prove that for all real numbers r, s, t, and u:

(r + s)(t + u) = rt + ru + st + su

Commutative Axiom for Multiplication:

For any two real numbers r and s, the following equation holds:

rs = sr

Commutative Axiom for Addition:

For any two real numbers r and s, the following equation holds:

r+s = s+r

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For any three real numbers a, b, c, we have two distributive axioms for multiplication over ...

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Proof without using commutative axioms is typified.

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