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受欢迎的代数 >

因式分解 0.008f^6+g^3h^9

解答

因式分解

0.008 f^{6} + g^{3} h^{9}

解答

(0.2 f^{2} + g h^{3}) (0.04 f^{4} - 0.2 f^{2} g h^{3} + g^{2} h^{6})

求解步骤

0.008 f^{6} + g^{3} h^{9}

将

g^{3} h^{9}

改写为

(g h^{3})^{3}

= 0.008 f^{6} + (g h^{3})^{3}

将

0.008 f^{6} + (g h^{3})^{3}

改写为

(3 0.008 f^{2})^{3} + (g h^{3})^{3}

= (3 0.008 f^{2})^{3} + (g h^{3})^{3}

使用立方和公式:

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

(3 0.008 f^{2})^{3} + (g h^{3})^{3} = (3 0.008 f^{2} + g h^{3}) ((3 0.008)^{2} f^{4} - 3 0.008 f^{2} g h^{3} + (g h^{3})^{2})

= (3 0.008 f^{2} + g h^{3}) ((3 0.008)^{2} f^{4} - 3 0.008 f^{2} g h^{3} + (g h^{3})^{2})

整理后得

= (3 0.008 f^{2} + g h^{3}) (0.00 8^{\frac{2}{3}} f^{4} - 3 0.008 f^{2} g h^{3} + (g h^{3})^{2})

化简

(3 0.008 f^{2} + g h^{3}) (0.00 8^{\frac{2}{3}} f^{4} - 3 0.008 f^{2} g h^{3} + (g h^{3})^{2}) : (3 0.008 f^{2} + g h^{3}) (0.00 8^{\frac{2}{3}} f^{4} - 3 0.008 f^{2} g h^{3} + g^{2} h^{6})

= (3 0.008 f^{2} + g h^{3}) (0.00 8^{\frac{2}{3}} f^{4} - 3 0.008 f^{2} g h^{3} + g^{2} h^{6})

3 0.008 = 0.2

= (0.2 f^{2} + g h^{3}) (0.00 8^{\frac{2}{3}} f^{4} - 3 0.008 f^{2} g h^{3} + g^{2} h^{6})

0.00 8^{\frac{2}{3}} = 0.04

= (0.2 f^{2} + g h^{3}) (0.04 f^{4} - 3 0.008 f^{2} g h^{3} + g^{2} h^{6})

3 0.008 = 0.2

= (0.2 f^{2} + g h^{3}) (0.04 f^{4} - 0.2 f^{2} g h^{3} + g^{2} h^{6})

流行的例子

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f (x) = [cos (x) + sin (x)]

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s im pl i f y V (2.6)