What is expand e^x(1-e^{2x}+2e^xy-y^2) ?

The solution to expand e^x(1-e^{2x}+2e^xy-y^2) is e^x-e^{3x}+2e^{2x}y-e^xy^2

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

expand

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

e^{x} - e^{3 x} + 2 e^{2 x} y - e^{x} y^{2}

Solution steps

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

Distribute parentheses

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

Apply minus-plus rules

+ (- a) = - a

= 1 \cdot e^{x} - e^{x} e^{2 x} + 2 e^{x} e^{x} y - e^{x} y^{2}

Simplify

1 \cdot e^{x} - e^{x} e^{2 x} + 2 e^{x} e^{x} y - e^{x} y^{2} : e^{x} - e^{3 x} + 2 e^{2 x} y - e^{x} y^{2}

= e^{x} - e^{3 x} + 2 e^{2 x} y - e^{x} y^{2}

\frac{f or ( x - 1 )}{x - 1}

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

\frac{9}{( 1 - x ) ^{2}}

\frac{n y ^{2} x}{( n x + a - 1 ) ^{2}}

\frac{s + 1}{s ^{2} ( s ^{2} + 1 )}

What is expand e^x(1-e^{2x}+2e^xy-y^2) ?
The solution to expand e^x(1-e^{2x}+2e^xy-y^2) is e^x-e^{3x}+2e^{2x}y-e^xy^2