因数 100x^{2a-2b}-49y^{4c}

解

因数

100 x^{2 a - 2 b} - 49 y^{4 c}

(10 x^{a - b} + 7 y^{2 c}) (10 x^{a - b} - 7 y^{2 c})

解答ステップ

100 x^{2 a - 2 b} - 49 y^{4 c}

x^{2 a - 2 b} = x^{2 (a - b)}

= 100 x^{2 (a - b)} - 49 y^{4 c}

100 x^{2 (a - b)}

を書き換え

(10 x^{1 (a - b)})^{2}

49 y^{4 c}

を書き換え

(7 y^{2 c})^{2}

= (10 x^{1 \cdot (a - b)})^{2} - (7 y^{2 c})^{2}

2乗の差の公式を適用する:

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

(10 x^{1 (a - b)})^{2} - (7 y^{2 c})^{2} = (10 x^{1 (a - b)} + 7 y^{2 c}) (10 x^{1 (a - b)} - 7 y^{2 c})

= (10 x^{1 (a - b)} + 7 y^{2 c}) (10 x^{1 (a - b)} - 7 y^{2 c})

改良

= (10 x^{a - b} + 7 y^{2 c}) (10 x^{a - b} - 7 y^{2 c})