因数 64v^2-25w^2

解

因数

64 v^{2} - 25 w^{2}

(8 v + 5 w) (8 v - 5 w)

解答ステップ

64 v^{2} - 25 w^{2}

64 v^{2} = (8 v)^{2}

25 w^{2} = (5 w)^{2}

= (8 v)^{2} - (5 w)^{2}

2乗の差の公式を適用する:

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

(8 v)^{2} - (5 w)^{2} = (8 v + 5 w) (8 v - 5 w)

= (8 v + 5 w) (8 v - 5 w)