A Ring is Commutative iff (a - b)(a + b) = a^2 - b^2 Proof

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A Ring is Commutative iff (a - b)(a + b) = a^2 - b^2 Proof. A proof that (a - b)(a + b) = a^2 - b^2 for all a, b in R if and only if R is a commutative ring.
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this was so straightforward, thanks!!!

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For a, b∈R, Prove that 1/2(a+b)^2 1/2 (a^2+b^2)

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