What is (x_{0}+sqrt(α)x_{1})^2 ?

The solution to (x_{0}+sqrt(α)x_{1})^2 is x_{0}^2+2x_{0}x_{1}sqrt(α)+αx_{1}^2

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simplify (x_{0}+sqrt(α)x_{1})^2

simplify

(x_{0} + α x_{1})^{2}

x_{0}^{2} + 2 x_{0} x_{1} α + α x_{1}^{2}

Solution steps

(x_{0} + α x_{1})^{2}

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

(x_{0} + α x_{1})^{2} = x_{0}^{2} + 2 x_{0} α x_{1} + (α x_{1})^{2}

= x_{0}^{2} + 2 x_{0} α x_{1} + (α x_{1})^{2}

2 x_{0} α x_{1} = 2 x_{0} x_{1} α

(α x_{1})^{2} = α x_{1}^{2}

= x_{0}^{2} + 2 x_{0} x_{1} α + α x_{1}^{2}

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What is (x_{0}+sqrt(α)x_{1})^2 ?
The solution to (x_{0}+sqrt(α)x_{1})^2 is x_{0}^2+2x_{0}x_{1}sqrt(α)+αx_{1}^2