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Popular >

expand t^2(at+b)e^t

Solution

expand

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

Solution

e^{t} t^{3} a + e^{t} t^{2} b

Solution steps

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

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

Apply the distributive law:

a (b + c) = ab + a c

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

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

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

e^{t} t^{2} t a = e^{t} t^{3} a

= e^{t} t^{3} a + e^{t} t^{2} b

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Frequently Asked Questions (FAQ)

What is expand t^2(at+b)e^t ?
The solution to expand t^2(at+b)e^t is e^tt^3a+e^tt^2b