展开 (4ab^2-3c^4)^3

解答

展开

(4 a b^{2} - 3 c^{4})^{3}

64 a^{3} b^{6} - 144 a^{2} b^{4} c^{4} + 108 a b^{2} c^{8} - 27 c^{12}

求解步骤

(4 a b^{2} - 3 c^{4})^{3}

使用完全立方公式:

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

(4 a b^{2} - 3 c^{4})^{3} = (4 a b^{2})^{3} - 3 (4 a b^{2})^{2} \cdot 3 c^{4} + 3 \cdot 4 a b^{2} (3 c^{4})^{2} - (3 c^{4})^{3}

= (4 a b^{2})^{3} - 3 (4 a b^{2})^{2} \cdot 3 c^{4} + 3 \cdot 4 a b^{2} (3 c^{4})^{2} - (3 c^{4})^{3}

化简

(4 a b^{2})^{3} - 3 (4 a b^{2})^{2} \cdot 3 c^{4} + 3 \cdot 4 a b^{2} (3 c^{4})^{2} - (3 c^{4})^{3} : 64 a^{3} b^{6} - 144 a^{2} b^{4} c^{4} + 108 a b^{2} c^{8} - 27 c^{12}

= 64 a^{3} b^{6} - 144 a^{2} b^{4} c^{4} + 108 a b^{2} c^{8} - 27 c^{12}

s im pl i f y ∣ - 3 + 2 ∣

\frac{6}{7} \div \frac{1}{6}

s im pl i f y - 12 (5 x - 4)

s im pl i f y \frac{x}{x + 1} - 1

s im pl i f y 38125