展开 x^2(x+3)e^x

解答

展开

x^{2} (x + 3) e^{x}

e^{x} x^{3} + 3 e^{x} x^{2}

求解步骤

x^{2} (x + 3) e^{x}

= e^{x} x^{2} (x + 3)

使用分配律:

a (b + c) = ab + a c

a = x^{2} e^{x}, b = x, c = 3

= x^{2} e^{x} x + x^{2} e^{x} \cdot 3

= e^{x} x^{2} x + 3 e^{x} x^{2}

e^{x} x^{2} x = e^{x} x^{3}

= e^{x} x^{3} + 3 e^{x} x^{2}

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