What is expand-1/4 (x^2+1)e^{2x} ?

The solution to expand-1/4 (x^2+1)e^{2x} is -(e^{2x}x^2)/4-(e^{2x})/4

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expand-1/4 (x^2+1)e^{2x}

expand

- \frac{1}{4} (x^{2} + 1) e^{2 x}

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

Solution steps

- \frac{1}{4} (x^{2} + 1) e^{2 x}

= - \frac{1}{4} e^{2 x} (x^{2} + 1)

Apply the distributive law:

a (b + c) = ab + a c

a = - \frac{1}{4} e^{2 x}, b = x^{2}, c = 1

= - \frac{1}{4} e^{2 x} x^{2} + (- \frac{1}{4} e^{2 x}) \cdot 1

Apply minus-plus rules

+ (- a) = - a

= - \frac{1}{4} e^{2 x} x^{2} - 1 \cdot \frac{1}{4} e^{2 x}

Simplify

- \frac{1}{4} e^{2 x} x^{2} - 1 \cdot \frac{1}{4} e^{2 x} : - \frac{e ^{2 x} x ^{2}}{4} - \frac{e ^{2 x}}{4}

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

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

- \frac{2 x}{( x ^{2} + c ) ^{2}}

(x - y = 5,) (x + 2 y = 7)

\frac{x}{( x - 2 ) ( x - 3 ) ( s - 6 )}

\frac{( 4 x - 1000 ) ^{2}}{9}

What is expand-1/4 (x^2+1)e^{2x} ?
The solution to expand-1/4 (x^2+1)e^{2x} is -(e^{2x}x^2)/4-(e^{2x})/4