因数 0.064x^{27}-1.331b^{15}

解

因数

0.064 x^{27} - 1.331 b^{15}

(0.4 x^{9} - 1.1 b^{5}) (0.16 x^{18} + 0.44 b^{5} x^{9} + 1.21 b^{10})

解答ステップ

0.064 x^{27} - 1.331 b^{15}

0.064 x^{27} - 1.331 b^{15}

を書き換え

(3 0.064 x^{9})^{3} - (3 1.331 b^{5})^{3}

= (3 0.064 x^{9})^{3} - (3 1.331 b^{5})^{3}

立方数の差の公式を適用する:

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

(3 0.064 x^{9})^{3} - (3 1.331 b^{5})^{3} = (3 0.064 x^{9} - 3 1.331 b^{5}) ((3 0.064)^{2} x^{18} + 3 0.064 3 1.331 x^{9} b^{5} + (3 1.331)^{2} b^{10})

= (3 0.064 x^{9} - 3 1.331 b^{5}) ((3 0.064)^{2} x^{18} + 3 0.064 3 1.331 x^{9} b^{5} + (3 1.331)^{2} b^{10})

改良

= (3 0.064 x^{9} - 3 1.331 b^{5}) (0.06 4^{\frac{2}{3}} x^{18} + 3 0.085184 x^{9} b^{5} + 1.33 1^{\frac{2}{3}} b^{10})

3 0.064 = 0.4

= (0.4 x^{9} - 3 1.331 b^{5}) (0.06 4^{\frac{2}{3}} x^{18} + 3 0.085184 b^{5} x^{9} + 1.33 1^{\frac{2}{3}} b^{10})

3 1.331 = 1.1

= (0.4 x^{9} - 1.1 b^{5}) (0.06 4^{\frac{2}{3}} x^{18} + 3 0.085184 b^{5} x^{9} + 1.33 1^{\frac{2}{3}} b^{10})

0.06 4^{\frac{2}{3}} = 0.16

= (0.4 x^{9} - 1.1 b^{5}) (0.16 x^{18} + 3 0.085184 b^{5} x^{9} + 1.33 1^{\frac{2}{3}} b^{10})

3 0.085184 = 0.44

= (0.4 x^{9} - 1.1 b^{5}) (0.16 x^{18} + 0.44 b^{5} x^{9} + 1.33 1^{\frac{2}{3}} b^{10})

1.33 1^{\frac{2}{3}} = 1.21

= (0.4 x^{9} - 1.1 b^{5}) (0.16 x^{18} + 0.44 b^{5} x^{9} + 1.21 b^{10})