What is expand (e^{(hw)/(kT)}-1)^2 ?

The solution to expand (e^{(hw)/(kT)}-1)^2 is e^{(2hw)/(kT)}-2e^{(hw)/(kT)}+1

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expand (e^{(hw)/(kT)}-1)^2

expand

(e^{\frac{h w}{k T}} - 1)^{2}

e^{\frac{2 h w}{k T}} - 2 e^{\frac{h w}{k T}} + 1

Solution steps

(e^{\frac{h w}{k T}} - 1)^{2}

Apply Perfect Square Formula:

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

a = e^{\frac{h w}{k T}}, b = 1

= (e^{\frac{h w}{k T}})^{2} - 2 e^{\frac{h w}{k T}} \cdot 1 + 1^{2}

Simplify

(e^{\frac{h w}{k T}})^{2} - 2 e^{\frac{h w}{k T}} \cdot 1 + 1^{2} : e^{\frac{2 h w}{k T}} - 2 e^{\frac{h w}{k T}} + 1

= e^{\frac{2 h w}{k T}} - 2 e^{\frac{h w}{k T}} + 1

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What is expand (e^{(hw)/(kT)}-1)^2 ?
The solution to expand (e^{(hw)/(kT)}-1)^2 is e^{(2hw)/(kT)}-2e^{(hw)/(kT)}+1