因数 3x^3y^2-9x^2y^4+3xy^3

解

因数

3 x^{3} y^{2} - 9 x^{2} y^{4} + 3 x y^{3}

3 x y^{2} (x^{2} - 3 x y^{2} + y)

解答ステップ

3 x^{3} y^{2} - 9 x^{2} y^{4} + 3 x y^{3}

指数の規則を適用する:

a^{b + c} = a^{b} a^{c}

x^{3} y^{2} = x x^{2} y^{2}, x^{2} y^{4} = xx y^{2} y^{2}, x y^{3} = x y^{2} y

= 3 x x^{2} y^{2} - 9 xx y^{2} y^{2} + 3 x y^{2} y

- 9

を書き換え

3 \cdot 3

= 3 x x^{2} y^{2} + 3 \cdot 3 xx y^{2} y^{2} + 3 x y^{2} y

共通項をくくり出す

3 x y^{2}

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