因数 w^6-z^6

解

因数

w^{6} - z^{6}

(w + z) (w^{2} - w z + z^{2}) (w - z) (w^{2} + w z + z^{2})

解答ステップ

w^{6} - z^{6}

w^{6} = (w^{3})^{2}

z^{6} = (z^{3})^{2}

= (w^{3})^{2} - (z^{3})^{2}

2乗の差の公式を適用する:

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

(w^{3})^{2} - (z^{3})^{2} = (w^{3} + z^{3}) (w^{3} - z^{3})

= (w^{3} + z^{3}) (w^{3} - z^{3})

因数

w^{3} + z^{3} : (w + z) (w^{2} - w z + z^{2})

= (w + z) (w^{2} - w z + z^{2}) (w^{3} - z^{3})

因数

w^{3} - z^{3} : (w - z) (w^{2} + w z + z^{2})

= (w + z) (w^{2} - w z + z^{2}) (w - z) (w^{2} + w z + z^{2})