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

The solution to expand 4e^x(e^{2x}-e^x) is 4e^{3x}-4e^{2x}

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

expand

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

4 e^{3 x} - 4 e^{2 x}

Solution steps

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

Apply the distributive law:

a (b - c) = ab - a c

a = 4 e^{x}, b = e^{2 x}, c = e^{x}

= 4 e^{x} e^{2 x} - 4 e^{x} e^{x}

Simplify

4 e^{x} e^{2 x} - 4 e^{x} e^{x} : 4 e^{3 x} - 4 e^{2 x}

= 4 e^{3 x} - 4 e^{2 x}

l im x \Rightarrow 2 (3 x^{2} - 5 x + 2)

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What is expand 4e^x(e^{2x}-e^x) ?
The solution to expand 4e^x(e^{2x}-e^x) is 4e^{3x}-4e^{2x}