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

The solution to expand 3(e^t-1)^2 is 3e^{2t}-6e^t+3

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expand 3(e^t-1)^2

expand

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

3 e^{2 t} - 6 e^{t} + 3

Solution steps

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

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

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

Distribute parentheses

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

Apply minus-plus rules

+ (- a) = - a

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

Simplify

3 e^{2 t} - 3 \cdot 2 e^{t} + 3 \cdot 1 : 3 e^{2 t} - 6 e^{t} + 3

= 3 e^{2 t} - 6 e^{t} + 3

(e^{j t} - e^{- j t})^{5}

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\frac{d}{d x} ((2 - x^{2}) cos (x^{2})) + 2 x sin (x^{2})

(1 + tan (x))^{3}

\frac{( ( 3 s - 1 ) ( 2 s - 1 ) )}{( s ( s ^{2} - 2 s + 14 ) )}