What is expand 4e^{2x}(e^{2x}-1)^2 ?

The solution to expand 4e^{2x}(e^{2x}-1)^2 is 4e^{6x}-8e^{4x}+4e^{2x}

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expand 4e^{2x}(e^{2x}-1)^2

expand

4 e^{2 x} (e^{2 x} - 1)^{2}

4 e^{6 x} - 8 e^{4 x} + 4 e^{2 x}

Solution steps

4 e^{2 x} (e^{2 x} - 1)^{2}

(e^{2 x} - 1)^{2} = e^{4 x} - 2 e^{2 x} + 1

= 4 e^{2 x} (e^{4 x} - 2 e^{2 x} + 1)

Distribute parentheses

= 4 e^{2 x} e^{4 x} + 4 e^{2 x} (- 2 e^{2 x}) + 4 e^{2 x} \cdot 1

Apply minus-plus rules

+ (- a) = - a

= 4 e^{2 x} e^{4 x} - 4 \cdot 2 e^{2 x} e^{2 x} + 4 \cdot 1 \cdot e^{2 x}

Simplify

4 e^{2 x} e^{4 x} - 4 \cdot 2 e^{2 x} e^{2 x} + 4 \cdot 1 \cdot e^{2 x} : 4 e^{6 x} - 8 e^{4 x} + 4 e^{2 x}

= 4 e^{6 x} - 8 e^{4 x} + 4 e^{2 x}

\frac{5 - 5 x}{2 ( 2 - x )}

(- e^{- 2 t} - 1)^{3}

e x (3 - i)^{6}

vx (x^{2} + v x^{2} - 2 v^{2} x^{2}) d x

(y - e^{- y}) (e^{y}) + e + y

What is expand 4e^{2x}(e^{2x}-1)^2 ?
The solution to expand 4e^{2x}(e^{2x}-1)^2 is 4e^{6x}-8e^{4x}+4e^{2x}