What is expand 1/5 e^x(e^x-1) ?

The solution to expand 1/5 e^x(e^x-1) is 1/5 e^{2x}-1/5 e^x

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expand 1/5 e^x(e^x-1)

expand

\frac{1}{5} e^{x} (e^{x} - 1)

\frac{1}{5} e^{2 x} - \frac{1}{5} e^{x}

Solution steps

\frac{1}{5} e^{x} (e^{x} - 1)

Apply the distributive law:

a (b - c) = ab - a c

a = \frac{1}{5} e^{x}, b = e^{x}, c = 1

= \frac{1}{5} e^{x} e^{x} - \frac{1}{5} e^{x} \cdot 1

= \frac{1}{5} e^{x} e^{x} - 1 \cdot \frac{1}{5} e^{x}

Simplify

\frac{1}{5} e^{x} e^{x} - 1 \cdot \frac{1}{5} e^{x} : \frac{1}{5} e^{2 x} - \frac{1}{5} e^{x}

= \frac{1}{5} e^{2 x} - \frac{1}{5} e^{x}

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

\frac{a + b}{2 ( a - b )}

\frac{- x ^{2} + 2 x - 5}{( x - 2 ) ^{2} ( x + 3 ) ^{2}}

\frac{s + 13}{( s + 1 ) ^{2} \cdot ( s + 5 )}

- 6 + i^{335} + 8 i^{87} + - 121

What is expand 1/5 e^x(e^x-1) ?
The solution to expand 1/5 e^x(e^x-1) is 1/5 e^{2x}-1/5 e^x