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

The solution to expand (2e^{4t}-4e^{-3t})^2 is 4e^{8t}-16e^t+16e^{-6t}

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

expand

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

4 e^{8 t} - 16 e^{t} + 16 e^{- 6 t}

Solution steps

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

Apply Perfect Square Formula:

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

a = 2 e^{4 t}, b = 4 e^{- 3 t}

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

Simplify

(2 e^{4 t})^{2} - 2 \cdot 2 e^{4 t} \cdot 4 e^{- 3 t} + (4 e^{- 3 t})^{2} : 4 e^{8 t} - 16 e^{t} + 16 e^{- 6 t}

= 4 e^{8 t} - 16 e^{t} + 16 e^{- 6 t}

ln (\frac{x ^{8}}{( x - 3 ) ^{4}})

\frac{( 1 - 4 ^{k + 1} )}{- 3}

π (16 - x^{2})^{2}

\frac{6 + 8 i}{4 + ( x + 3 ) i}

2 (ln (x))

What is expand (2e^{4t}-4e^{-3t})^2 ?
The solution to expand (2e^{4t}-4e^{-3t})^2 is 4e^{8t}-16e^t+16e^{-6t}