展开 20(4x^3-3x)^{19}(12x^2-3)

解答

展开

20 (4 x^{3} - 3 x)^{19} (12 x^{2} - 3)

20 \cdot 12 x^{2} (4 x^{3} - 3 x)^{19} - 20 \cdot 3 (4 x^{3} - 3 x)^{19}

求解步骤

20 (4 x^{3} - 3 x)^{19} (12 x^{2} - 3)

使用分配律:

a (b - c) = ab - a c

a = 20 (4 x^{3} - 3 x)^{19}, b = 12 x^{2}, c = 3

= 20 (4 x^{3} - 3 x)^{19} \cdot 12 x^{2} - 20 (4 x^{3} - 3 x)^{19} \cdot 3

= 20 \cdot 12 x^{2} (4 x^{3} - 3 x)^{19} - 20 \cdot 3 (4 x^{3} - 3 x)^{19}

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e x p an d n gu l a r (- 2, - \frac{π}{3})

e x p an d (k + 1)! \cdot (k + 2)

e x p an d \frac{v ^{3}}{( v ^{2} + 1 ) ( 2 v ^{2} + 1 )}

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