Statistics - Covariance and variance question

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Please fill in the intermediate steps $$\sum_{i=1}^nx_i(x_i-\bar x)=\sum_{i=1}^n(x_i-\bar x)^2$$ and $$\sum_{i=1}^nx_i(y_i-\bar y)=\sum_{i=1}^n(x_i-\bar x)(y_i-\bar y)$$

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Hint: Use the fact that $\bar{x}\sum_{i=1}^n(x_i-\bar{x})=0$.