What is expand (y^3)(e^t+te^t) ?

The solution to expand (y^3)(e^t+te^t) is e^ty^3+e^ty^3t

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expand (y^3)(e^t+te^t)

expand

(y^{3}) (e^{t} + t e^{t})

e^{t} y^{3} + e^{t} y^{3} t

Solution steps

(y^{3}) (e^{t} + t e^{t})

= (y^{3}) (e^{t} + e^{t} t)

Apply the distributive law:

a (b + c) = ab + a c

a = (y^{3}), b = e^{t}, c = t e^{t}

= (y^{3}) e^{t} + (y^{3}) t e^{t}

= e^{t} (y^{3}) + e^{t} t (y^{3})

Remove parentheses:

(a) = a

= e^{t} y^{3} + e^{t} y^{3} t

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\frac{( s ^{3} + 11 s ^{2} - s + 1 )}{s ( s - 1 ) ( s ^{2} - 36 )}

What is expand (y^3)(e^t+te^t) ?
The solution to expand (y^3)(e^t+te^t) is e^ty^3+e^ty^3t