Explain this inequality in PDEs, Elliptic Operators (Folland)

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I am reading Gerald Follands Introduction To PDEs, and I got to this part:

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The part in red is a bit confusing, I am not sure how it follows from the sentences afterwards. I get that both are non-zero and homogenous, which means that we can somehow "standardize" the sum, but I am not sure how this follows for general alpha.