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

The solution to expand (3e^{3t}+4e^{-4t})^3 is 27e^{9t}+108e^{2t}+144e^{-5t}+64e^{-12t}

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

expand

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

27 e^{9 t} + 108 e^{2 t} + 144 e^{- 5 t} + 64 e^{- 12 t}

Solution steps

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

Apply Perfect Cube Formula:

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

a = 3 e^{3 t}, b = 4 e^{- 4 t}

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

Simplify

(3 e^{3 t})^{3} + 3 (3 e^{3 t})^{2} \cdot 4 e^{- 4 t} + 3 \cdot 3 e^{3 t} (4 e^{- 4 t})^{2} + (4 e^{- 4 t})^{3} : 27 e^{9 t} + 108 e^{2 t} + 144 e^{- 5 t} + 64 e^{- 12 t}

= 27 e^{9 t} + 108 e^{2 t} + 144 e^{- 5 t} + 64 e^{- 12 t}

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

(e^{t} - 1)^{3}

\frac{1 + 6 x}{( 4 x - 3 ) ( 2 x + 5 )}

\frac{x ^{2} - 3 x + 10}{( x - 2 ) ( x ^{2} + 4 )}

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

What is expand (3e^{3t}+4e^{-4t})^3 ?
The solution to expand (3e^{3t}+4e^{-4t})^3 is 27e^{9t}+108e^{2t}+144e^{-5t}+64e^{-12t}