What is expand (3+7e^{-0.25x})^2 ?

The solution to expand (3+7e^{-0.25x})^2 is 9+42e^{-0.25x}+49e^{-0.5x}

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expand (3+7e^{-0.25x})^2

expand

(3 + 7 e^{- 0.25 x})^{2}

9 + 42 e^{- 0.25 x} + 49 e^{- 0.5 x}

Solution steps

(3 + 7 e^{- 0.25 x})^{2}

Apply Perfect Square Formula:

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

a = 3, b = 7 e^{- 0.25 x}

= 3^{2} + 2 \cdot 3 \cdot 7 e^{- 0.25 x} + (7 e^{- 0.25 x})^{2}

Simplify

3^{2} + 2 \cdot 3 \cdot 7 e^{- 0.25 x} + (7 e^{- 0.25 x})^{2} : 9 + 42 e^{- 0.25 x} + 49 e^{- 0.5 x}

= 9 + 42 e^{- 0.25 x} + 49 e^{- 0.5 x}

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What is expand (3+7e^{-0.25x})^2 ?
The solution to expand (3+7e^{-0.25x})^2 is 9+42e^{-0.25x}+49e^{-0.5x}