因数-7x^4y^2+14xy^3+21xy^4

解

因数

- 7 x^{4} y^{2} + 14 x y^{3} + 21 x y^{4}

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

解答ステップ

- 7 x^{4} y^{2} + 14 x y^{3} + 21 x y^{4}

指数の規則を適用する:

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

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

= - 7 x x^{3} y^{2} + 14 x y^{2} y + 21 x y^{2} y^{2}

21

を書き換え

3 \cdot 7

14

を書き換え

2 \cdot 7

= - 7 x x^{3} y^{2} + 2 \cdot 7 x y^{2} y + 3 \cdot 7 x y^{2} y^{2}

共通項をくくり出す

7 x y^{2}

= 7 x y^{2} (- x^{3} + 2 y + 3 y^{2})