What is expand l[(1+e^{2t})^2] ?

The solution to expand l[(1+e^{2t})^2] is l+2le^{2t}+le^{4t}

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expand l[(1+e^{2t})^2]

expand

l [(1 + e^{2 t})^{2}]

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

Solution steps

l ((1 + e^{2 t})^{2})

Remove parentheses:

(a) = a

= l (1 + e^{2 t})^{2}

(1 + e^{2 t})^{2} = 1 + 2 e^{2 t} + e^{4 t}

= l (2 e^{2 t} + e^{4 t} + 1)

Distribute parentheses

= l \cdot 1 + l \cdot 2 e^{2 t} + l e^{4 t}

= 1 \cdot l + 2 l e^{2 t} + l e^{4 t}

Multiply:

1 \cdot l = l

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

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What is expand l[(1+e^{2t})^2] ?
The solution to expand l[(1+e^{2t})^2] is l+2le^{2t}+le^{4t}