What is expand (t^2-7t+e^t)(U(t-5)) ?

The solution to expand (t^2-7t+e^t)(U(t-5)) is t^3U-12t^2U+35tU+e^ttU-5e^tU

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expand (t^2-7t+e^t)(U(t-5))

expand

(t^{2} - 7 t + e^{t}) (U (t - 5))

t^{3} U - 12 t^{2} U + 35 t U + e^{t} t U - 5 e^{t} U

Solution steps

(t^{2} - 7 t + e^{t}) (U (t - 5))

Distribute parentheses

= (U (t - 5)) t^{2} + (U (t - 5)) (- 7 t) + (U (t - 5)) e^{t}

Apply minus-plus rules

+ (- a) = - a

= t^{2} (U (t - 5)) - 7 t (U (t - 5)) + e^{t} (U (t - 5))

Simplify

t^{2} (U (t - 5)) - 7 t (U (t - 5)) + e^{t} (U (t - 5)) : t^{3} U - 12 t^{2} U + 35 t U + e^{t} t U - 5 e^{t} U

= t^{3} U - 12 t^{2} U + 35 t U + e^{t} t U - 5 e^{t} U

\frac{250}{( x + 23.27 ) ( x + 476.73 )}

\frac{s ^{2} + 3 s - 7}{( s - 1 ) ( s ^{2} + 2 )}

\frac{1}{( 1 + 2 x ) ^{4}}

x (x^{6} + 1) d x + y^{2} (x^{4} + 1) d y

\frac{1}{4 ( x ^{2} + x + 3 ) ^{4}}

What is expand (t^2-7t+e^t)(U(t-5)) ?
The solution to expand (t^2-7t+e^t)(U(t-5)) is t^3U-12t^2U+35tU+e^ttU-5e^tU