What is expand (2e^{-4t}+2)^3 ?

The solution to expand (2e^{-4t}+2)^3 is 8e^{-12t}+24e^{-8t}+24e^{-4t}+8

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expand (2e^{-4t}+2)^3

expand

(2 e^{- 4 t} + 2)^{3}

8 e^{- 12 t} + 24 e^{- 8 t} + 24 e^{- 4 t} + 8

Solution steps

(2 e^{- 4 t} + 2)^{3}

Apply Perfect Cube Formula:

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

a = 2 e^{- 4 t}, b = 2

= (2 e^{- 4 t})^{3} + 3 (2 e^{- 4 t})^{2} \cdot 2 + 3 \cdot 2 e^{- 4 t} \cdot 2^{2} + 2^{3}

Simplify

(2 e^{- 4 t})^{3} + 3 (2 e^{- 4 t})^{2} \cdot 2 + 3 \cdot 2 e^{- 4 t} \cdot 2^{2} + 2^{3} : 8 e^{- 12 t} + 24 e^{- 8 t} + 24 e^{- 4 t} + 8

= 8 e^{- 12 t} + 24 e^{- 8 t} + 24 e^{- 4 t} + 8

\frac{x}{4 ( x + 4 )}

\frac{1}{( y - 4 ) ( y - 7 )}

\frac{2 + x ^{2}}{( x + 4 ) ( x ^{2} + 3 )}

\frac{( x + 1 ) ( x + 2 )}{( x - 9 ) ( x + 9 )}

e (x - 3) (x^{2} + 2)^{'}

What is expand (2e^{-4t}+2)^3 ?
The solution to expand (2e^{-4t}+2)^3 is 8e^{-12t}+24e^{-8t}+24e^{-4t}+8