What is expand (e^{2t}+1)^3 ?

The solution to expand (e^{2t}+1)^3 is e^{6t}+3e^{4t}+3e^{2t}+1

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

expand

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

e^{6 t} + 3 e^{4 t} + 3 e^{2 t} + 1

Solution steps

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

Apply Perfect Cube Formula:

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

a = e^{2 t}, b = 1

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

Simplify

(e^{2 t})^{3} + 3 (e^{2 t})^{2} \cdot 1 + 3 e^{2 t} \cdot 1^{2} + 1^{3} : e^{6 t} + 3 e^{4 t} + 3 e^{2 t} + 1

= e^{6 t} + 3 e^{4 t} + 3 e^{2 t} + 1

cos (2) (x - 1) - 1

\frac{1}{4} cos (2 θ) (3 + cos (4 θ))

\frac{w ( t - w )}{4 tan ( \frac{θ}{2} )}

x (x - 5) (x + 5 - 22) (x + 5 + 22)

100 (\frac{b ^{2}}{8} + 75 (\frac{b}{2} + 25))

What is expand (e^{2t}+1)^3 ?
The solution to expand (e^{2t}+1)^3 is e^{6t}+3e^{4t}+3e^{2t}+1