What is expand (12-12e^{-t/x})^2 ?

The solution to expand (12-12e^{-t/x})^2 is 144-288e^{-t/x}+144e^{-(2t)/x}

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expand (12-12e^{-t/x})^2

expand

(12 - 12 e^{- \frac{t}{x}})^{2}

144 - 288 e^{- \frac{t}{x}} + 144 e^{- \frac{2 t}{x}}

Solution steps

(12 - 12 e^{- \frac{t}{x}})^{2}

Apply Perfect Square Formula:

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

a = 12, b = 12 e^{- \frac{t}{x}}

= 1 2^{2} - 2 \cdot 12 \cdot 12 e^{- \frac{t}{x}} + (12 e^{- \frac{t}{x}})^{2}

Simplify

1 2^{2} - 2 \cdot 12 \cdot 12 e^{- \frac{t}{x}} + (12 e^{- \frac{t}{x}})^{2} : 144 - 288 e^{- \frac{t}{x}} + 144 e^{- \frac{2 t}{x}}

= 144 - 288 e^{- \frac{t}{x}} + 144 e^{- \frac{2 t}{x}}

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What is expand (12-12e^{-t/x})^2 ?
The solution to expand (12-12e^{-t/x})^2 is 144-288e^{-t/x}+144e^{-(2t)/x}