因数 (x^3)/(64)-y^6

解

因数

\frac{x ^{3}}{64} - y^{6}

(\frac{x}{4} - y^{2}) (\frac{x y ^{2}}{4} + \frac{x ^{2}}{16} + y^{4})

解答ステップ

\frac{x ^{3}}{64} - y^{6}

\frac{x ^{3}}{64} - y^{6}

を書き換え

(3 \frac{1}{64} x)^{3} - (y^{2})^{3}

= (3 \frac{1}{64} x)^{3} - (y^{2})^{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 \frac{1}{64} x)^{3} - (y^{2})^{3} = (3 \frac{1}{64} x - y^{2}) (3 \frac{1}{64})^{2} x^{2} + 3 \frac{1}{64} x y^{2} + y^{4}

= (3 \frac{1}{64} x - y^{2}) (3 \frac{1}{64})^{2} x^{2} + 3 \frac{1}{64} x y^{2} + y^{4}

改良

= (\frac{x}{4} - y^{2}) (\frac{x y ^{2}}{4} + \frac{x ^{2}}{16} + y^{4})