What is expand (6+e^{-5t})^2 ?

The solution to expand (6+e^{-5t})^2 is 36+12e^{-5t}+e^{-10t}

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expand (6+e^{-5t})^2

expand

(6 + e^{- 5 t})^{2}

36 + 12 e^{- 5 t} + e^{- 10 t}

Solution steps

(6 + e^{- 5 t})^{2}

Apply Perfect Square Formula:

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

a = 6, b = e^{- 5 t}

= 6^{2} + 2 \cdot 6 e^{- 5 t} + (e^{- 5 t})^{2}

Simplify

6^{2} + 2 \cdot 6 e^{- 5 t} + (e^{- 5 t})^{2} : 36 + 12 e^{- 5 t} + e^{- 10 t}

= 36 + 12 e^{- 5 t} + e^{- 10 t}

\frac{4 x ^{2} - 10 x - 20}{( 4 x - 5 ) ^{2}}

\frac{2 x ^{3} - 4 x ^{2} - 15 x + 9}{( x - 1 ) ^{2}}

\frac{- 12 x ^{2} - 16 x - 27}{( 4 x ^{2} - 9 ) ^{2}}

A (2, \frac{3}{4}) B (\frac{3}{5}, - \frac{1}{2})

3 (x + Δ x)^{3} - 2 (x + Δ x) + (x + Δ x)^{5} - 2

What is expand (6+e^{-5t})^2 ?
The solution to expand (6+e^{-5t})^2 is 36+12e^{-5t}+e^{-10t}