What is expand (2e^{-t}+2)^2 ?

The solution to expand (2e^{-t}+2)^2 is 4e^{-2t}+8e^{-t}+4

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expand (2e^{-t}+2)^2

expand

(2 e^{- t} + 2)^{2}

4 e^{- 2 t} + 8 e^{- t} + 4

Solution steps

(2 e^{- t} + 2)^{2}

Apply Perfect Square Formula:

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

a = 2 e^{- t}, b = 2

= (2 e^{- t})^{2} + 2 \cdot 2 e^{- t} \cdot 2 + 2^{2}

Simplify

(2 e^{- t})^{2} + 2 \cdot 2 e^{- t} \cdot 2 + 2^{2} : 4 e^{- 2 t} + 8 e^{- t} + 4

= 4 e^{- 2 t} + 8 e^{- t} + 4

tan (\frac{1}{2}) (A - B)

- \frac{2 m}{5} (10 m + 5 n - 15 p)

(\frac{m}{k} - k) (2 m - 1)

\frac{d}{d p} ((h) (60 h^{5} + 2 - p^{3}))

\frac{d ^{2}}{d x ^{2}} ((y) (5 x^{2} - 3) (7 x^{3} + x))

What is expand (2e^{-t}+2)^2 ?
The solution to expand (2e^{-t}+2)^2 is 4e^{-2t}+8e^{-t}+4