What is expand (e^{2x}(5e^{3x}-2))/(25) ?

The solution to expand (e^{2x}(5e^{3x}-2))/(25) is (e^{5x})/5-(2e^{2x})/(25)

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expand (e^{2x}(5e^{3x}-2))/(25)

expand

\frac{e ^{2 x} ( 5 e ^{3 x} - 2 )}{25}

\frac{e ^{5 x}}{5} - \frac{2 e ^{2 x}}{25}

Solution steps

\frac{e ^{2 x} ( 5 e ^{3 x} - 2 )}{25}

Expand

e^{2 x} (5 e^{3 x} - 2) : 5 e^{5 x} - 2 e^{2 x}

= \frac{5 e ^{5 x} - 2 e ^{2 x}}{25}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{5 e ^{5 x} - 2 e ^{2 x}}{25} = \frac{5 e ^{5 x}}{25} - \frac{2 e ^{2 x}}{25}

= \frac{5 e ^{5 x}}{25} - \frac{2 e ^{2 x}}{25}

Cancel

\frac{5 e ^{5 x}}{25} : \frac{e ^{5 x}}{5}

= \frac{e ^{5 x}}{5} - \frac{2 e ^{2 x}}{25}

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What is expand (e^{2x}(5e^{3x}-2))/(25) ?
The solution to expand (e^{2x}(5e^{3x}-2))/(25) is (e^{5x})/5-(2e^{2x})/(25)