What is expand t^2(1+e^{-at}) ?

The solution to expand t^2(1+e^{-at}) is t^2+e^{-ta}t^2

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expand t^2(1+e^{-at})

expand

t^{2} (1 + e^{- a t})

t^{2} + e^{- t a} t^{2}

Solution steps

t^{2} (1 + e^{- a t})

= t^{2} (1 + e^{- t a})

Apply the distributive law:

a (b + c) = ab + a c

a = t^{2}, b = 1, c = e^{- a t}

= t^{2} \cdot 1 + t^{2} e^{- a t}

= 1 \cdot t^{2} + e^{- t a} t^{2}

Multiply:

1 \cdot t^{2} = t^{2}

= t^{2} + e^{- t a} t^{2}

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

(1 + x^{2}) d y + 2 x y d x

(x + i y) (x - i y)^{2}

What is expand t^2(1+e^{-at}) ?
The solution to expand t^2(1+e^{-at}) is t^2+e^{-ta}t^2