Solved – Deduction of the expectation for lack of fit test

I don't understand that in the answer of 4.21,why $(E(y_{ij}))^2$ is lost when calculating $E(y_{ij}^2)$ which is shown in the third row. What's more, in the last row, where does the second term come from?
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I think there is a typo in your solution.

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