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

The solution to expand (e^{3t}-1)^3 is e^{9t}-3e^{6t}+3e^{3t}-1

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

expand

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

e^{9 t} - 3 e^{6 t} + 3 e^{3 t} - 1

Solution steps

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

Apply Perfect Cube Formula:

(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

a = e^{3 t}, b = 1

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

Simplify

(e^{3 t})^{3} - 3 (e^{3 t})^{2} \cdot 1 + 3 e^{3 t} \cdot 1^{2} - 1^{3} : e^{9 t} - 3 e^{6 t} + 3 e^{3 t} - 1

= e^{9 t} - 3 e^{6 t} + 3 e^{3 t} - 1

(8.35, - 18.93) x (- 18.93, 7.6) x (2.48, - 8.35)

\frac{( x ^{3} + x ^{2} + 21 )}{x ( 2 x - 5 ) ^{3} ( x ^{2} + 2 x + 5 ) ^{2}}

(f (x) + g (x)) x^{'}

\frac{( x - 2 ) \cdot ( 2 x + 1 )}{x + 1}

What is expand (e^{3t}-1)^3 ?
The solution to expand (e^{3t}-1)^3 is e^{9t}-3e^{6t}+3e^{3t}-1