What is expand (Ax^2+Bx+C)e^{3x} ?

The solution to expand (Ax^2+Bx+C)e^{3x} is Ae^{3x}x^2+Be^{3x}x+Ce^{3x}

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expand (Ax^2+Bx+C)e^{3x}

expand

(A x^{2} + B x + C) e^{3 x}

A e^{3 x} x^{2} + B e^{3 x} x + C e^{3 x}

Solution steps

(A x^{2} + B x + C) e^{3 x}

= e^{3 x} (A x^{2} + B x + C)

Distribute parentheses

= e^{3 x} A x^{2} + e^{3 x} B x + e^{3 x} C

= A e^{3 x} x^{2} + B e^{3 x} x + C e^{3 x}

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What is expand (Ax^2+Bx+C)e^{3x} ?
The solution to expand (Ax^2+Bx+C)e^{3x} is Ae^{3x}x^2+Be^{3x}x+Ce^{3x}