What is expand (1-t)(2e^tt^2+t^3) ?

The solution to expand (1-t)(2e^tt^2+t^3) is 2e^tt^2+t^3-2e^tt^3-t^4

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expand (1-t)(2e^tt^2+t^3)

expand

(1 - t) (2 e^{t} t^{2} + t^{3})

2 e^{t} t^{2} + t^{3} - 2 e^{t} t^{3} - t^{4}

Solution steps

(1 - t) (2 e^{t} t^{2} + t^{3})

Apply FOIL method:

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

a = 1, b = - t, c = 2 e^{t} t^{2}, d = t^{3}

= 1 \cdot 2 e^{t} t^{2} + 1 \cdot t^{3} + (- t) \cdot 2 e^{t} t^{2} + (- t) t^{3}

Apply minus-plus rules

+ (- a) = - a

= 1 \cdot 2 e^{t} t^{2} + 1 \cdot t^{3} - 2 e^{t} t^{2} t - t^{3} t

Simplify

1 \cdot 2 e^{t} t^{2} + 1 \cdot t^{3} - 2 e^{t} t^{2} t - t^{3} t : 2 e^{t} t^{2} + t^{3} - 2 e^{t} t^{3} - t^{4}

= 2 e^{t} t^{2} + t^{3} - 2 e^{t} t^{3} - t^{4}

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What is expand (1-t)(2e^tt^2+t^3) ?
The solution to expand (1-t)(2e^tt^2+t^3) is 2e^tt^2+t^3-2e^tt^3-t^4