展开 (2x^2-3y)^3

解答

展开

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

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

求解步骤

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

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

化简

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

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

f a c t or 2 x^{3} - 5 x^{2} - 4 x + 10

s im pl i f y 8 \frac{n ^{18} p ^{7}}{n ^{2} p ^{- 1}}

s im pl i f y \frac{- 4 x ^{8} y ^{4}}{12 x ^{2} y}

s im pl i f y \frac{3}{4} + \frac{2}{3} + \frac{1}{2}

e x p an d (x + 6) (2 x + 4)