因数 16x^{2n}-1

解

因数

16 x^{2 n} - 1

(4 x^{n} + 1) (4 x^{n} - 1)

解答ステップ

16 x^{2 n} - 1

16 x^{2 n}

を書き換え

(2^{2} x^{1 n})^{2}

= (2^{2} x^{1 \cdot n})^{2} - 1

1

を書き換え

1^{2}

= (2^{2} x^{1 n})^{2} - 1^{2}

2乗の差の公式を適用する:

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

(2^{2} x^{1 n})^{2} - 1^{2} = (2^{2} x^{1 n} + 1) (2^{2} x^{1 n} - 1)

= (2^{2} x^{1 n} + 1) (2^{2} x^{1 n} - 1)

改良

= (4 x^{n} + 1) (4 x^{n} - 1)