因式分解 81a^6-4b^2c^8

解答

因式分解

81 a^{6} - 4 b^{2} c^{8}

(9 a^{3} + 2 b c^{4}) (9 a^{3} - 2 b c^{4})

求解步骤

81 a^{6} - 4 b^{2} c^{8}

81 a^{6} = (9 a^{3})^{2}

4 b^{2} c^{8} = (2 b c^{4})^{2}

= (9 a^{3})^{2} - (2 b c^{4})^{2}

使用平方差公式:

x^{2} - y^{2} = (x + y) (x - y)

(9 a^{3})^{2} - (2 b c^{4})^{2} = (9 a^{3} + 2 b c^{4}) (9 a^{3} - 2 b c^{4})

= (9 a^{3} + 2 b c^{4}) (9 a^{3} - 2 b c^{4})

\frac{1}{2} - \frac{1}{8} q = \frac{q - 1}{4}

x^{3} - 3 x^{2} - 9 x + 27 < 0

6 (r - 2) = 2 r + 8

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

\frac{2 x - 1}{x - 1} = 3