展开 (2x^{1/2}-3z^{2/3})^3

解答

展开

(2 x^{\frac{1}{2}} - 3 z^{\frac{2}{3}})^{3}

8 x^{\frac{3}{2}} - 36 x z^{\frac{2}{3}} + 54 x^{\frac{1}{2}} z^{\frac{4}{3}} - 27 z^{2}

求解步骤

(2 x^{\frac{1}{2}} - 3 z^{\frac{2}{3}})^{3}

使用完全立方公式:

(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

(2 x^{\frac{1}{2}} - 3 z^{\frac{2}{3}})^{3} = (2 x^{\frac{1}{2}})^{3} - 3 (2 x^{\frac{1}{2}})^{2} \cdot 3 z^{\frac{2}{3}} + 3 \cdot 2 x^{\frac{1}{2}} (3 z^{\frac{2}{3}})^{2} - (3 z^{\frac{2}{3}})^{3}

= (2 x^{\frac{1}{2}})^{3} - 3 (2 x^{\frac{1}{2}})^{2} \cdot 3 z^{\frac{2}{3}} + 3 \cdot 2 x^{\frac{1}{2}} (3 z^{\frac{2}{3}})^{2} - (3 z^{\frac{2}{3}})^{3}

(2 x^{\frac{1}{2}})^{3} = 8 x^{\frac{3}{2}}

3 (2 x^{\frac{1}{2}})^{2} \cdot 3 z^{\frac{2}{3}} = 36 x z^{\frac{2}{3}}

3 \cdot 2 x^{\frac{1}{2}} (3 z^{\frac{2}{3}})^{2} = 54 x^{\frac{1}{2}} z^{\frac{4}{3}}

(3 z^{\frac{2}{3}})^{3} = 27 z^{2}

= 8 x^{\frac{3}{2}} - 36 x z^{\frac{2}{3}} + 54 x^{\frac{1}{2}} z^{\frac{4}{3}} - 27 z^{2}

e x p an d - \frac{h}{x ( x + h )}

e x p an d \frac{π ( e - 1 )}{4}

e x p an d sin (x) (1 + csc (x))

e x p an d \frac{( x ^{3} - 2 )}{( 4 x + 3 ) ( 6 x - 2 )}

e x p an d (6 + sinh (x))^{2}