What is expand (3ay+Ce^{6x})^3 ?

The solution to expand (3ay+Ce^{6x})^3 is 27a^3y^3+27a^2Ce^{6x}y^2+9aC^2e^{12x}y+C^3e^{18x}

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expand (3ay+Ce^{6x})^3

expand

(3 a y + C e^{6 x})^{3}

27 a^{3} y^{3} + 27 a^{2} C e^{6 x} y^{2} + 9 a C^{2} e^{12 x} y + C^{3} e^{18 x}

Solution steps

(3 a y + C e^{6 x})^{3}

Apply Perfect Cube Formula:

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

a = 3 a y, b = C e^{6 x}

= (3 a y)^{3} + 3 (3 a y)^{2} C e^{6 x} + 3 \cdot 3 a y (C e^{6 x})^{2} + (C e^{6 x})^{3}

Simplify

(3 a y)^{3} + 3 (3 a y)^{2} C e^{6 x} + 3 \cdot 3 a y (C e^{6 x})^{2} + (C e^{6 x})^{3} : 27 a^{3} y^{3} + 27 a^{2} C e^{6 x} y^{2} + 9 a C^{2} e^{12 x} y + C^{3} e^{18 x}

= 27 a^{3} y^{3} + 27 a^{2} C e^{6 x} y^{2} + 9 a C^{2} e^{12 x} y + C^{3} e^{18 x}

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What is expand (3ay+Ce^{6x})^3 ?
The solution to expand (3ay+Ce^{6x})^3 is 27a^3y^3+27a^2Ce^{6x}y^2+9aC^2e^{12x}y+C^3e^{18x}