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

The solution to expand (2e^t+1)^3 is 8e^{3t}+12e^{2t}+6e^t+1

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expand (2e^t+1)^3

expand

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

8 e^{3 t} + 12 e^{2 t} + 6 e^{t} + 1

Solution steps

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

Apply Perfect Cube Formula:

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

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

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

Simplify

(2 e^{t})^{3} + 3 (2 e^{t})^{2} \cdot 1 + 3 \cdot 2 e^{t} \cdot 1^{2} + 1^{3} : 8 e^{3 t} + 12 e^{2 t} + 6 e^{t} + 1

= 8 e^{3 t} + 12 e^{2 t} + 6 e^{t} + 1

sin (x) (tan (x) + 1) (tan (x) - 1)

(4 - 3 i) l e f t (5 - i) l e f t (1 + i)

6 (\frac{1}{2})^{4} + 2 (\frac{1}{2})^{3} - 12 (\frac{1}{2})^{2} + 3

\frac{( s + 0.1 ) ( s + 500 )}{( s + 30 ) ^{2}}

ro t a c i o na l (x^{2} - 2 y^{2} + 4)

What is expand (2e^t+1)^3 ?
The solution to expand (2e^t+1)^3 is 8e^{3t}+12e^{2t}+6e^t+1