展开 (x^2+2x)((2x+2)e^{x^2+2x})

解答

展开

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

2 e^{x^{2} + 2 x} x^{3} + 6 e^{x^{2} + 2 x} x^{2} + 4 e^{x^{2} + 2 x} x

求解步骤

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

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

使用分配律:

a (b + c) = ab + a c

a = ((2 x + 2) e^{x^{2} + 2 x}), b = x^{2}, c = 2 x

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

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

化简

x^{2} (e^{x^{2} + 2 x} (2 x + 2)) + 2 x (e^{x^{2} + 2 x} (2 x + 2)) : 2 e^{x^{2} + 2 x} x^{3} + 6 e^{x^{2} + 2 x} x^{2} + 4 e^{x^{2} + 2 x} x

= 2 e^{x^{2} + 2 x} x^{3} + 6 e^{x^{2} + 2 x} x^{2} + 4 e^{x^{2} + 2 x} x

e x p an d lo g_{10} (8 \frac{s}{t})

e x p an d (sin (θ) + cos (θ)) (sin (x) - cos (x))

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e x p an d (1 - 2 cos (x) + cos (2 x))^{2}

e x p an d (tan^{(2)} (y) - cot^{(2)} (y))^{(2)}