展开 4(x^3+2x-\sqrt[3]{x}+1)^3

解答

展开

4 (x^{3} + 2 x - 3 x + 1)^{3}

4 x^{9} + 24 x^{7} - 12 x^{6} 3 x + 12 x^{6} + 48 x^{5} - 48 x^{4} 3 x + 48 x^{4} - 24 x^{3} 3 x + 44 x^{3} - 48 x^{2} 3 x + 48 x^{2} - 48 x 3 x + 24 x + 12 x^{\frac{11}{3}} + 24 x^{\frac{5}{3}} - 4 x^{\frac{2}{3}} 3 x + 12 x^{\frac{2}{3}} - 12 3 x + 4

求解步骤

4 (x^{3} + 2 x - 3 x + 1)^{3}

(x^{3} + 2 x - 3 x + 1)^{3} = x^{9} + 6 x^{7} - 3 x^{6} 3 x + 3 x^{6} + 12 x^{5} - 12 x^{4} 3 x + 12 x^{4} - 6 x^{3} 3 x + 11 x^{3} - 12 x^{2} 3 x + 12 x^{2} - 12 x 3 x + 6 x + 3 x^{\frac{11}{3}} + 6 x^{\frac{5}{3}} - x^{\frac{2}{3}} 3 x + 3 x^{\frac{2}{3}} - 3 3 x + 1

= 4 (x^{9} + 6 x^{7} + 3 x^{6} - 3 x^{6} 3 x + 12 x^{5} + 12 x^{4} - 12 x^{4} 3 x + 11 x^{3} - 6 x^{3} 3 x + 12 x^{2} - 12 x^{2} 3 x + 6 x - 12 x 3 x + 3 x^{\frac{11}{3}} + 6 x^{\frac{5}{3}} + 3 x^{\frac{2}{3}} - x^{\frac{2}{3}} 3 x - 3 3 x + 1)

打开括号

= 4 x^{9} + 4 \cdot 6 x^{7} + 4 (- 3 x^{6} 3 x) + 4 \cdot 3 x^{6} + 4 \cdot 12 x^{5} + 4 (- 12 x^{4} 3 x) + 4 \cdot 12 x^{4} + 4 (- 6 x^{3} 3 x) + 4 \cdot 11 x^{3} + 4 (- 12 x^{2} 3 x) + 4 \cdot 12 x^{2} + 4 (- 12 x 3 x) + 4 \cdot 6 x + 4 \cdot 3 x^{\frac{11}{3}} + 4 \cdot 6 x^{\frac{5}{3}} + 4 (- x^{\frac{2}{3}} 3 x) + 4 \cdot 3 x^{\frac{2}{3}} + 4 (- 3 3 x) + 4 \cdot 1

使用加减运算法则

+ (- a) = - a

= 4 x^{9} + 4 \cdot 6 x^{7} - 4 \cdot 3 x^{6} 3 x + 4 \cdot 3 x^{6} + 4 \cdot 12 x^{5} - 4 \cdot 12 x^{4} 3 x + 4 \cdot 12 x^{4} - 4 \cdot 6 x^{3} 3 x + 4 \cdot 11 x^{3} - 4 \cdot 12 x^{2} 3 x + 4 \cdot 12 x^{2} - 4 \cdot 12 x 3 x + 4 \cdot 6 x + 4 \cdot 3 x^{\frac{11}{3}} + 4 \cdot 6 x^{\frac{5}{3}} - 4 x^{\frac{2}{3}} 3 x + 4 \cdot 3 x^{\frac{2}{3}} - 4 \cdot 3 3 x + 4 \cdot 1

化简

4 x^{9} + 4 \cdot 6 x^{7} - 4 \cdot 3 x^{6} 3 x + 4 \cdot 3 x^{6} + 4 \cdot 12 x^{5} - 4 \cdot 12 x^{4} 3 x + 4 \cdot 12 x^{4} - 4 \cdot 6 x^{3} 3 x + 4 \cdot 11 x^{3} - 4 \cdot 12 x^{2} 3 x + 4 \cdot 12 x^{2} - 4 \cdot 12 x 3 x + 4 \cdot 6 x + 4 \cdot 3 x^{\frac{11}{3}} + 4 \cdot 6 x^{\frac{5}{3}} - 4 x^{\frac{2}{3}} 3 x + 4 \cdot 3 x^{\frac{2}{3}} - 4 \cdot 3 3 x + 4 \cdot 1 : 4 x^{9} + 24 x^{7} - 12 x^{6} 3 x + 12 x^{6} + 48 x^{5} - 48 x^{4} 3 x + 48 x^{4} - 24 x^{3} 3 x + 44 x^{3} - 48 x^{2} 3 x + 48 x^{2} - 48 x 3 x + 24 x + 12 x^{\frac{11}{3}} + 24 x^{\frac{5}{3}} - 4 x^{\frac{2}{3}} 3 x + 12 x^{\frac{2}{3}} - 12 3 x + 4

= 4 x^{9} + 24 x^{7} - 12 x^{6} 3 x + 12 x^{6} + 48 x^{5} - 48 x^{4} 3 x + 48 x^{4} - 24 x^{3} 3 x + 44 x^{3} - 48 x^{2} 3 x + 48 x^{2} - 48 x 3 x + 24 x + 12 x^{\frac{11}{3}} + 24 x^{\frac{5}{3}} - 4 x^{\frac{2}{3}} 3 x + 12 x^{\frac{2}{3}} - 12 3 x + 4

e x p an d (- 7, - 5, 18) (y)

e x p an d A (- 2, 3) y B (5, - 4)

e x p an d \frac{d}{d x} ((2 - x) e^{x}) - x - 2

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

e x p an d - 2 sin (2 (x - 45)) + 1