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受欢迎的代数 >

因式分解 1000a^6-343b^3c^6

解答

因式分解

1000 a^{6} - 343 b^{3} c^{6}

解答

(10 a^{2} - 7 b c^{2}) (100 a^{4} + 70 a^{2} b c^{2} + 49 b^{2} c^{4})

求解步骤

1000 a^{6} - 343 b^{3} c^{6}

将

1000 a^{6}

改写为

(10 a^{2})^{3}

将

343 b^{3} c^{6}

改写为

(7 b c^{2})^{3}

= (10 a^{2})^{3} - (7 b c^{2})^{3}

使用立方差公式:

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

(10 a^{2})^{3} - (7 b c^{2})^{3} = (10 a^{2} - 7 b c^{2}) ((10 a^{2})^{2} + 10 a^{2} 7 b c^{2} + (7 b c^{2})^{2})

= (10 a^{2} - 7 b c^{2}) ((10 a^{2})^{2} + 10 a^{2} 7 b c^{2} + (7 b c^{2})^{2})

化简

(10 a^{2} - 7 b c^{2}) ((10 a^{2})^{2} + 10 a^{2} \cdot 7 b c^{2} + (7 b c^{2})^{2}) : (10 a^{2} - 7 b c^{2}) (100 a^{4} + 70 a^{2} b c^{2} + 49 b^{2} c^{4})

= (10 a^{2} - 7 b c^{2}) (100 a^{4} + 70 a^{2} b c^{2} + 49 b^{2} c^{4})

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