What is factor e^{s+t}-e^{2s+t} ?

The solution to factor e^{s+t}-e^{2s+t} is e^{t+s}(1-e^s)

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factor e^{s+t}-e^{2s+t}

factor

e^{s + t} - e^{2 s + t}

e^{t + s} (1 - e^{s})

Solution steps

e^{s + t} - e^{2 s + t}

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

= e^{t} e^{s} - e^{t} e^{2 s}

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

e^{2 s} = e^{s} e^{s}

= e^{s} e^{t} - e^{s} e^{s} e^{t}

Factor out common term

e^{t} e^{s}

= e^{t} e^{s} (1 - e^{s})

Refine

= e^{s + t} (- e^{s} + 1)

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What is factor e^{s+t}-e^{2s+t} ?
The solution to factor e^{s+t}-e^{2s+t} is e^{t+s}(1-e^s)