因数 50x^3+160x^2y+128xy^2

解

因数

50 x^{3} + 160 x^{2} y + 128 x y^{2}

2 x (5 x + 8 y)^{2}

解答ステップ

50 x^{3} + 160 x^{2} y + 128 x y^{2}

共通項をくくり出す

2 x : 2 x (25 x^{2} + 80 x y + 64 y^{2})

= 2 x (25 x^{2} + 80 x y + 64 y^{2})

因数

25 x^{2} + 80 x y + 64 y^{2} : (5 x + 8 y) (5 x + 8 y)

= 2 x (5 x + 8 y) (5 x + 8 y)

指数の規則を適用する:

aa = a^{2}

(5 x + 8 y) (5 x + 8 y) = (5 x + 8 y)^{2}

= 2 x (5 x + 8 y)^{2}