因数 15x^3y^5-25x^4y^2+10x^6y^4

解

因数

15 x^{3} y^{5} - 25 x^{4} y^{2} + 10 x^{6} y^{4}

5 x^{3} y^{2} (3 y^{3} - 5 x + 2 x^{3} y^{2})

解答ステップ

15 x^{3} y^{5} - 25 x^{4} y^{2} + 10 x^{6} y^{4}

指数の規則を適用する:

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

x^{3} y^{5} = x^{3} y^{2} y^{3}, x^{4} y^{2} = x^{3} x y^{2}, x^{6} y^{4} = x^{3} x^{3} y^{2} y^{2}

= 15 x^{3} y^{2} y^{3} - 25 x^{3} x y^{2} + 10 x^{3} x^{3} y^{2} y^{2}

10

を書き換え

2 \cdot 5

- 25

を書き換え

5 \cdot 5

= 3 \cdot 5 x^{3} y^{2} y^{3} + 5 \cdot 5 x^{3} x y^{2} + 2 \cdot 5 x^{3} x^{3} y^{2} y^{2}

共通項をくくり出す

5 x^{3} y^{2}

= 5 x^{3} y^{2} (3 y^{3} - 5 x + 2 x^{3} y^{2})