What is expand (te^t+te^{2t})^2 ?

The solution to expand (te^t+te^{2t})^2 is e^{2t}t^2+2e^{3t}t^2+e^{4t}t^2

Popular >

expand (te^t+te^{2t})^2

expand

(t e^{t} + t e^{2 t})^{2}

e^{2 t} t^{2} + 2 e^{3 t} t^{2} + e^{4 t} t^{2}

Solution steps

(t e^{t} + t e^{2 t})^{2}

= (e^{t} t + e^{2 t} t)^{2}

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

a = t e^{t}, b = t e^{2 t}

= (t e^{t})^{2} + 2 t e^{t} t e^{2 t} + (t e^{2 t})^{2}

Simplify

(t e^{t})^{2} + 2 t e^{t} t e^{2 t} + (t e^{2 t})^{2} : e^{2 t} t^{2} + 2 e^{3 t} t^{2} + e^{4 t} t^{2}

= e^{2 t} t^{2} + 2 e^{3 t} t^{2} + e^{4 t} t^{2}

- \frac{40 ( - 3 x ^{2} - 4 )}{( x ^{2} - 4 ) ^{3}}

\frac{d}{d x} ((1 - x^{2}) arctan (x)) - x

\frac{2 x ( - x \frac{d y}{d x} + y )}{y ^{3}}

\frac{( x + 2 ) ( x - 3 )}{x}

\frac{x ( 2 x ^{3} + y )}{6 y ^{2}}

What is expand (te^t+te^{2t})^2 ?
The solution to expand (te^t+te^{2t})^2 is e^{2t}t^2+2e^{3t}t^2+e^{4t}t^2