因数 w^{3x}+8

解

因数

w^{3 x} + 8

(w^{x} + 2) (w^{2 x} - 2 w^{x} + 4)

解答ステップ

w^{3 x} + 8

指数の規則を適用する:

a^{b c} = (a^{b})^{c}

w^{3 x} = (w^{x})^{3}

= (w^{x})^{3} + 8

8

を書き換え

2^{3}

= (w^{x})^{3} + 2^{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})

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

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

改良

= (w^{x} + 2) ((w^{x})^{2} - 2 w^{x} + 4)

簡素化

(w^{x} + 2) ((w^{x})^{2} - 2 w^{x} + 4) : (w^{x} + 2) (w^{2 x} - 2 w^{x} + 4)

= (w^{x} + 2) (w^{2 x} - 2 w^{x} + 4)