What is expand (b+e^{-t})^3 ?

The solution to expand (b+e^{-t})^3 is b^3+3e^{-t}b^2+3e^{-2t}b+e^{-3t}

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expand (b+e^{-t})^3

expand

(b + e^{- t})^{3}

b^{3} + 3 e^{- t} b^{2} + 3 e^{- 2 t} b + e^{- 3 t}

Solution steps

(b + e^{- t})^{3}

Apply Perfect Cube Formula:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

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

= b^{3} + 3 b^{2} e^{- t} + 3 b (e^{- t})^{2} + (e^{- t})^{3}

Simplify

b^{3} + 3 b^{2} e^{- t} + 3 b (e^{- t})^{2} + (e^{- t})^{3} : b^{3} + 3 e^{- t} b^{2} + 3 e^{- 2 t} b + e^{- 3 t}

= b^{3} + 3 e^{- t} b^{2} + 3 e^{- 2 t} b + e^{- 3 t}

l im x \Rightarrow 0 + (2 - e^{3} x) 15 x

(sin (x) - 1) (2 cos (x) + 1)

\frac{( s + 1 ) ( s + 5 )}{s ^{3} + 7 s ^{2} + 11 s + 3}

(y - cos^{2} (x)) d x + cos (x) d y

\frac{1}{s ( s ^{2} + 5 )}

What is expand (b+e^{-t})^3 ?
The solution to expand (b+e^{-t})^3 is b^3+3e^{-t}b^2+3e^{-2t}b+e^{-3t}