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

The solution to expand ((x^2+4x)^2)/(e^{2x)} is (x^4)/(e^{2x)}+(8x^3)/(e^{2x)}+(16x^2)/(e^{2x)}

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

expand

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

\frac{x ^{4}}{e ^{2 x}} + \frac{8 x ^{3}}{e ^{2 x}} + \frac{16 x ^{2}}{e ^{2 x}}

Solution steps

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

(x^{2} + 4 x)^{2} = x^{4} + 8 x^{3} + 16 x^{2}

= \frac{x ^{4} + 8 x ^{3} + 16 x ^{2}}{e ^{2 x}}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{x ^{4} + 8 x ^{3} + 16 x ^{2}}{e ^{2 x}} = \frac{x ^{4}}{e ^{2 x}} + \frac{8 x ^{3}}{e ^{2 x}} + \frac{16 x ^{2}}{e ^{2 x}}

= \frac{x ^{4}}{e ^{2 x}} + \frac{8 x ^{3}}{e ^{2 x}} + \frac{16 x ^{2}}{e ^{2 x}}

\frac{1}{( x + 5 ) ( x - 5 )}

\frac{d}{d θ} ((r (θ)) (1 - cos (θ)))

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

\frac{50}{( x + y ) ^{3}}

\frac{252 x}{( 4 + x ) ^{5}}

What is expand ((x^2+4x)^2)/(e^{2x)} ?
The solution to expand ((x^2+4x)^2)/(e^{2x)} is (x^4)/(e^{2x)}+(8x^3)/(e^{2x)}+(16x^2)/(e^{2x)}