展开 (2x^2-3y^3)^3

解答

展开

(2 x^{2} - 3 y^{3})^{3}

8 x^{6} - 36 x^{4} y^{3} + 54 x^{2} y^{6} - 27 y^{9}

求解步骤

(2 x^{2} - 3 y^{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^{2} - 3 y^{3})^{3} = (2 x^{2})^{3} - 3 (2 x^{2})^{2} \cdot 3 y^{3} + 3 \cdot 2 x^{2} (3 y^{3})^{2} - (3 y^{3})^{3}

= (2 x^{2})^{3} - 3 (2 x^{2})^{2} \cdot 3 y^{3} + 3 \cdot 2 x^{2} (3 y^{3})^{2} - (3 y^{3})^{3}

化简

(2 x^{2})^{3} - 3 (2 x^{2})^{2} \cdot 3 y^{3} + 3 \cdot 2 x^{2} (3 y^{3})^{2} - (3 y^{3})^{3} : 8 x^{6} - 36 x^{4} y^{3} + 54 x^{2} y^{6} - 27 y^{9}

= 8 x^{6} - 36 x^{4} y^{3} + 54 x^{2} y^{6} - 27 y^{9}

s im pl i f y (p - 4 t) + (3 t - 8 p) + (11 p + 5 t)

s im pl i f y 0.2 \cdot 0.2 \cdot 0.2

f a c t or 9 m^{2} - 1

s im pl i f y (32)^{\frac{- 2}{5}}

s im pl i f y 3 - (- 15)