因数 16x^6-49a^2*y^4

解

因数

16 x^{6} - 49 a^{2} \cdot y^{4}

(4 x^{3} + 7 a y^{2}) (4 x^{3} - 7 a y^{2})

解答ステップ

16 x^{6} - 49 a^{2} y^{4}

16 x^{6} = (4 x^{3})^{2}

49 a^{2} y^{4} = (7 a y^{2})^{2}

= (4 x^{3})^{2} - (7 a y^{2})^{2}

2乗の差の公式を適用する:

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

(4 x^{3})^{2} - (7 a y^{2})^{2} = (4 x^{3} + 7 a y^{2}) (4 x^{3} - 7 a y^{2})

= (4 x^{3} + 7 a y^{2}) (4 x^{3} - 7 a y^{2})