What is expand (e^{2AT}-1)^2 ?

The solution to expand (e^{2AT}-1)^2 is e^{4AT}-2e^{2AT}+1

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expand (e^{2AT}-1)^2

expand

(e^{2 A T} - 1)^{2}

e^{4 A T} - 2 e^{2 A T} + 1

Solution steps

(e^{2 A T} - 1)^{2}

Apply Perfect Square Formula:

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

a = e^{2 A T}, b = 1

= (e^{2 A T})^{2} - 2 e^{2 A T} \cdot 1 + 1^{2}

Simplify

(e^{2 A T})^{2} - 2 e^{2 A T} \cdot 1 + 1^{2} : e^{4 A T} - 2 e^{2 A T} + 1

= e^{4 A T} - 2 e^{2 A T} + 1

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What is expand (e^{2AT}-1)^2 ?
The solution to expand (e^{2AT}-1)^2 is e^{4AT}-2e^{2AT}+1