# Proof without using commutative axioms

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

https://brainmass.com/math/discrete-math/proof-without-commutative-axioms-365508

#### Solution Preview

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

#### Solution Summary

Proof without using commutative axioms is typified.

$2.19