因数 4x^{2a}-25y^4

解

因数

4 x^{2 a} - 25 y^{4}

(2 x^{a} + 5 y^{2}) (2 x^{a} - 5 y^{2})

解答ステップ

4 x^{2 a} - 25 y^{4}

4 x^{2 a}

を書き換え

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

25 y^{4}

を書き換え

(5 y^{2})^{2}

= (2 x^{1 \cdot a})^{2} - (5 y^{2})^{2}

2乗の差の公式を適用する:

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

(2 x^{1 a})^{2} - (5 y^{2})^{2} = (2 x^{1 a} + 5 y^{2}) (2 x^{1 a} - 5 y^{2})

= (2 x^{1 a} + 5 y^{2}) (2 x^{1 a} - 5 y^{2})

改良

= (5 y^{2} + 2 x^{a}) (2 x^{a} - 5 y^{2})