What is expand (2Ax+B)e^x+e^x(Ax^2+Bx+C) ?

The solution to expand (2Ax+B)e^x+e^x(Ax^2+Bx+C) is 2Ae^xx+Be^x+Ae^xx^2+Be^xx+Ce^x

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expand (2Ax+B)e^x+e^x(Ax^2+Bx+C)

expand

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

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

Solution steps

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

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

Expand

e^{x} (2 A x + B) : 2 A e^{x} x + B e^{x}

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

Expand

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

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

\frac{( x ^{3} + 2 x ^{2} )}{( x + 1 ) ^{2}}

(\frac{5 x + 4}{x ^{2} - 4}) (\frac{4 x + 2}{x ^{2} - 4})

(R + \frac{t}{2})^{4}

\frac{a + 3}{( a + 8 ) ( a - 3 )}

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