因数 1/16 x^4-y^4

解

因数

\frac{1}{16} x^{4} - y^{4}

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

解答ステップ

\frac{1}{16} x^{4} - y^{4}

\frac{x ^{4}}{16} - y^{4}

を書き換え

(\frac{1}{16} x^{2})^{2} - (y^{2})^{2}

= (\frac{1}{16} x^{2})^{2} - (y^{2})^{2}

2乗の差の公式を適用する:

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

(\frac{1}{16} x^{2})^{2} - (y^{2})^{2} = (\frac{1}{16} x^{2} + y^{2}) (\frac{1}{16} x^{2} - y^{2})

= (\frac{1}{16} x^{2} + y^{2}) (\frac{1}{16} x^{2} - y^{2})

因数

\frac{1}{16} x^{2} - y^{2} : \frac{1}{16} x + y \frac{1}{16} x - y

= (\frac{1}{16} x^{2} + y^{2}) \frac{1}{16} x + y \frac{1}{16} x - y

改良

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