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受欢迎的代数 >

因式分解 x^{12}y^6+27z^3

解答

因式分解

x^{12} y^{6} + 27 z^{3}

解答

(x^{4} y^{2} + 3 z) (x^{8} y^{4} - 3 x^{4} y^{2} z + 9 z^{2})

求解步骤

x^{12} y^{6} + 27 z^{3}

将

x^{12} y^{6}

改写为

(x^{2} y)^{6}

将

27 z^{3}

改写为

(3 z)^{3}

= (x^{2} y)^{6} + (3 z)^{3}

使用指数法则:

a^{b c} = (a^{b})^{c}

(x^{2} y)^{6} = ((x^{2} y)^{2})^{3}

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

使用立方和公式:

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

((x^{2} y)^{2})^{3} + (3 z)^{3} = ((x^{2} y)^{2} + 3 z) ((x^{2} y)^{4} - 3 z (x^{2} y)^{2} + (3 z)^{2})

= (3 z + (x^{2} y)^{2}) ((3 z)^{2} - 3 z (x^{2} y)^{2} + (x^{2} y)^{4})

化简

((x^{2} y)^{2} + 3 z) ((x^{2} y)^{4} - 3 z (x^{2} y)^{2} + (3 z)^{2}) : (x^{4} y^{2} + 3 z) (x^{8} y^{4} - 3 x^{4} y^{2} z + 9 z^{2})

= (x^{4} y^{2} + 3 z) (x^{8} y^{4} - 3 x^{4} y^{2} z + 9 z^{2})

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