What is expand (4-e^{3x})^3 ?

The solution to expand (4-e^{3x})^3 is 64-48e^{3x}+12e^{6x}-e^{9x}

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expand (4-e^{3x})^3

expand

(4 - e^{3 x})^{3}

64 - 48 e^{3 x} + 12 e^{6 x} - e^{9 x}

Solution steps

(4 - e^{3 x})^{3}

Apply Perfect Cube Formula:

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

a = 4, b = e^{3 x}

= 4^{3} - 3 \cdot 4^{2} e^{3 x} + 3 \cdot 4 (e^{3 x})^{2} - (e^{3 x})^{3}

Simplify

4^{3} - 3 \cdot 4^{2} e^{3 x} + 3 \cdot 4 (e^{3 x})^{2} - (e^{3 x})^{3} : 64 - 48 e^{3 x} + 12 e^{6 x} - e^{9 x}

= 64 - 48 e^{3 x} + 12 e^{6 x} - e^{9 x}

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What is expand (4-e^{3x})^3 ?
The solution to expand (4-e^{3x})^3 is 64-48e^{3x}+12e^{6x}-e^{9x}