因数 8x^5y^3+32x^2y^8-64x^4y^2

解

因数

8 x^{5} y^{3} + 32 x^{2} y^{8} - 64 x^{4} y^{2}

8 x^{2} y^{2} (x^{3} y + 4 y^{6} - 8 x^{2})

解答ステップ

8 x^{5} y^{3} + 32 x^{2} y^{8} - 64 x^{4} y^{2}

指数の規則を適用する:

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

x^{5} y^{3} = x^{2} x^{3} y^{2} y, x^{2} y^{8} = x^{2} y^{2} y^{6}, x^{4} y^{2} = x^{2} x^{2} y^{2}

= 8 x^{2} x^{3} y^{2} y + 32 x^{2} y^{2} y^{6} - 64 x^{2} x^{2} y^{2}

- 64

を書き換え

8 \cdot 8

32

を書き換え

4 \cdot 8

= 8 x^{2} x^{3} y^{2} y + 4 \cdot 8 x^{2} y^{2} y^{6} + 8 \cdot 8 x^{2} x^{2} y^{2}

共通項をくくり出す

8 x^{2} y^{2}

= 8 x^{2} y^{2} (x^{3} y + 4 y^{6} - 8 x^{2})