因数 0.008a^6+b^3c^9

解

因数

0.008 a^{6} + b^{3} c^{9}

(0.2 a^{2} + b c^{3}) (0.04 a^{4} - 0.2 a^{2} b c^{3} + b^{2} c^{6})

解答ステップ

0.008 a^{6} + b^{3} c^{9}

b^{3} c^{9}

を書き換え

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

= 0.008 a^{6} + (b c^{3})^{3}

0.008 a^{6} + (b c^{3})^{3}

を書き換え

(3 0.008 a^{2})^{3} + (b c^{3})^{3}

= (3 0.008 a^{2})^{3} + (b c^{3})^{3}

立方数の和の公式を適用する:

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

(3 0.008 a^{2})^{3} + (b c^{3})^{3} = (3 0.008 a^{2} + b c^{3}) ((3 0.008)^{2} a^{4} - 3 0.008 a^{2} b c^{3} + (b c^{3})^{2})

= (3 0.008 a^{2} + b c^{3}) ((3 0.008)^{2} a^{4} - 3 0.008 a^{2} b c^{3} + (b c^{3})^{2})

改良

= (3 0.008 a^{2} + b c^{3}) (0.00 8^{\frac{2}{3}} a^{4} - 3 0.008 a^{2} b c^{3} + (b c^{3})^{2})

簡素化

(3 0.008 a^{2} + b c^{3}) (0.00 8^{\frac{2}{3}} a^{4} - 3 0.008 a^{2} b c^{3} + (b c^{3})^{2}) : (3 0.008 a^{2} + b c^{3}) (0.00 8^{\frac{2}{3}} a^{4} - 3 0.008 a^{2} b c^{3} + b^{2} c^{6})

= (3 0.008 a^{2} + b c^{3}) (0.00 8^{\frac{2}{3}} a^{4} - 3 0.008 a^{2} b c^{3} + b^{2} c^{6})

3 0.008 = 0.2

= (0.2 a^{2} + b c^{3}) (0.00 8^{\frac{2}{3}} a^{4} - 3 0.008 a^{2} b c^{3} + b^{2} c^{6})

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

= (0.2 a^{2} + b c^{3}) (0.04 a^{4} - 3 0.008 a^{2} b c^{3} + b^{2} c^{6})

3 0.008 = 0.2

= (0.2 a^{2} + b c^{3}) (0.04 a^{4} - 0.2 a^{2} b c^{3} + b^{2} c^{6})