What is factor e^{2x+y}-e^{2y+x} ?

The solution to factor e^{2x+y}-e^{2y+x} is e^{y+x}(e^x-e^y)

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factor e^{2x+y}-e^{2y+x}

factor

e^{2 x + y} - e^{2 y + x}

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

Solution steps

e^{2 x + y} - e^{2 y + x}

Apply exponent rule:

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

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

Apply exponent rule:

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

e^{2 x} = e^{x} e^{x}, e^{2 y} = e^{y} e^{y}

= e^{x} e^{x} e^{y} - e^{y} e^{y} e^{x}

Factor out common term

e^{y} e^{x}

= e^{y} e^{x} (e^{x} - e^{y})

Refine

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

sin^{(2)} (2 x)

1 - 2 l - l

- 3 x + (- 11)

sin (x) e^{x} - sin (x) e^{3 x}

x^{2 k + 2} - y^{2 k + 2}

What is factor e^{2x+y}-e^{2y+x} ?
The solution to factor e^{2x+y}-e^{2y+x} is e^{y+x}(e^x-e^y)