因数 49x^2y^6z^{10}-a^{12}

解

因数

49 x^{2} \cdot y^{6} \cdot z^{10} - a^{12}

(7 x y^{3} z^{5} + a^{6}) (7 x y^{3} z^{5} - a^{6})

解答ステップ

49 x^{2} y^{6} z^{10} - a^{12}

49 x^{2} y^{6} z^{10} = (7 x y^{3} z^{5})^{2}

a^{12} = (a^{6})^{2}

= (7 x y^{3} z^{5})^{2} - (a^{6})^{2}

2乗の差の公式を適用する:

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

(7 x y^{3} z^{5})^{2} - (a^{6})^{2} = (7 x y^{3} z^{5} + a^{6}) (7 x y^{3} z^{5} - a^{6})

= (7 x y^{3} z^{5} + a^{6}) (7 x y^{3} z^{5} - a^{6})