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

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

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

expand

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

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

Solution steps

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

Apply FOIL method:

(a + b) (c + d) = a c + a d + b c + b d

a = 1, b = y^{2}, c = e^{2 x}, d = - e^{y}

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

Apply minus-plus rules

+ (- a) = - a

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

Simplify

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

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

\frac{4 - x ^{2}}{2}

x (1 - cos (1) sin (1))

cos (x (1 - a))

\frac{2 ( 12 - Y )}{3}

- cos (0)

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