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

The solution to factor e^{2x+2y^2}-e^{2x+y^2} is e^{y^2+2x}(e^{y^2}-1)

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

factor

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

e^{y^{2} + 2 x} (e^{y^{2}} - 1)

Solution steps

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

Apply exponent rule:

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

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

Apply exponent rule:

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

e^{2 y^{2}} = e^{y^{2}} e^{y^{2}}

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

Factor out common term

e^{y^{2}} e^{2 x}

= e^{y^{2}} e^{2 x} (e^{y^{2}} - 1)

Refine

= e^{2 x + y^{2}} (e^{y^{2}} - 1)

f (c) = 5 + c

x \cdot e^{x y} + 3 x^{2} \cdot y

a^{3} b^{3} c^{3} - 64

3 sin (x^{2} - 1) - 5

2 + x - 2

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