What is expand (cos(t)+5e^{4t})^3 ?

The solution to expand (cos(t)+5e^{4t})^3 is cos^3(t)+15e^{4t}cos^2(t)+75e^{8t}cos(t)+125e^{12t}

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expand (cos(t)+5e^{4t})^3

expand

(cos (t) + 5 e^{4 t})^{3}

cos^{3} (t) + 15 e^{4 t} cos^{2} (t) + 75 e^{8 t} cos (t) + 125 e^{12 t}

Solution steps

(cos (t) + 5 e^{4 t})^{3}

Apply Perfect Cube Formula:

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

a = cos (t), b = 5 e^{4 t}

= cos^{3} (t) + 3 cos^{2} (t) \cdot 5 e^{4 t} + 3 cos (t) (5 e^{4 t})^{2} + (5 e^{4 t})^{3}

Simplify

cos^{3} (t) + 3 cos^{2} (t) \cdot 5 e^{4 t} + 3 cos (t) (5 e^{4 t})^{2} + (5 e^{4 t})^{3} : cos^{3} (t) + 15 e^{4 t} cos^{2} (t) + 75 e^{8 t} cos (t) + 125 e^{12 t}

= cos^{3} (t) + 15 e^{4 t} cos^{2} (t) + 75 e^{8 t} cos (t) + 125 e^{12 t}

(x + 25)^{2}

(cos (x) + i sin (x))^{3}

(- 5, 8) y (- 5, - 6)

(csc (x) + 1) tan (x) - sec (x)

(1 + i)^{9}

What is expand (cos(t)+5e^{4t})^3 ?
The solution to expand (cos(t)+5e^{4t})^3 is cos^3(t)+15e^{4t}cos^2(t)+75e^{8t}cos(t)+125e^{12t}