Let R b e a ommutative ring of hara teristi 3 and with unity and let a, b, c ∈R. Compute and simplify (a + b)3; hen e ompute and simplify (a + b)9

Question

Let R b e a ommutative ring of hara teristi 3 and with unity and let a, b, c ∈R. Compute and simplify (a + b)3; hen e ompute and simplify (a + b)9
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Solution 1

It seems like there are some typos in your question. I believe you're asking for the simplification of (a + b)³ and (a + b)⁹ in a commutative ring of characteristic 3. Here's how you can do it:

  1. (a + b)³:

Using the binomial theorem, we have (a + b)³ = a³ + 3a²b + 3ab² + b³.

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