What is expand (cx-x^2)(-te^{-t}+e^{-t}) ?

The solution to expand (cx-x^2)(-te^{-t}+e^{-t}) is -ce^{-t}xt+ce^{-t}x+e^{-t}x^2t-e^{-t}x^2

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expand (cx-x^2)(-te^{-t}+e^{-t})

expand

(c x - x^{2}) (- t e^{- t} + e^{- t})

- c e^{- t} x t + c e^{- t} x + e^{- t} x^{2} t - e^{- t} x^{2}

Solution steps

(c x - x^{2}) (- t e^{- t} + e^{- t})

= (c x - x^{2}) (- e^{- t} t + e^{- t})

Apply FOIL method:

(a + b) (c + d) = a c + a d + b c + b d

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

= c x (- t e^{- t}) + c x e^{- t} + (- x^{2}) (- t e^{- t}) + (- x^{2}) e^{- t}

Apply minus-plus rules

+ (- a) = - a, (- a) (- b) = ab

= - c e^{- t} x t + c e^{- t} x + e^{- t} x^{2} t - e^{- t} x^{2}

\frac{( 2 x ^{2} + 3 x + 7 )}{( x + 1 ) ^{2} ( x + 3 ) ^{'}}

(1 + 2 x - 3 x^{2})^{5}

\frac{2 ( 6 - 2 x ) ^{3}}{3}

2 (x + 9) - 18 ln (x + 9)

(x - a)^{2} e^{a - 3 x}

What is expand (cx-x^2)(-te^{-t}+e^{-t}) ?
The solution to expand (cx-x^2)(-te^{-t}+e^{-t}) is -ce^{-t}xt+ce^{-t}x+e^{-t}x^2t-e^{-t}x^2