因数 6(1-x)^2-4(1-x)^3-6x(1-x)^2-1

解

因数

6 (1 - x)^{2} - 4 (1 - x)^{3} - 6 x (1 - x)^{2} - 1

- 2 x^{3} + 6 x^{2} - 6 x + 1

解答ステップ

6 (1 - x)^{2} - 4 (1 - x)^{3} - 6 x (1 - x)^{2} - 1

(1 - x)^{2} : 1 - 2 x + x^{2}

= 6 (1 - 2 x + x^{2}) - 4 (1 - x)^{3} - 6 x (1 - x)^{2} - 1

(1 - x)^{3} : 1 - 3 x + 3 x^{2} - x^{3}

= 6 (1 - 2 x + x^{2}) - 4 (1 - 3 x + 3 x^{2} - x^{3}) - 6 x (1 - x)^{2} - 1

(1 - x)^{2} : 1 - 2 x + x^{2}

= 6 (1 - 2 x + x^{2}) - 4 (1 - 3 x + 3 x^{2} - x^{3}) - 6 x (1 - 2 x + x^{2}) - 1

拡張

6 (1 - 2 x + x^{2}) : 6 - 12 x + 6 x^{2}

= 6 - 12 x + 6 x^{2} - 4 (1 - 3 x + 3 x^{2} - x^{3}) - 6 x (1 - 2 x + x^{2}) - 1

拡張

- 4 (1 - 3 x + 3 x^{2} - x^{3}) : - 4 + 12 x - 12 x^{2} + 4 x^{3}

= 6 - 12 x + 6 x^{2} - 4 + 12 x - 12 x^{2} + 4 x^{3} - 6 x (1 - 2 x + x^{2}) - 1

拡張

- 6 x (1 - 2 x + x^{2}) : - 6 x + 12 x^{2} - 6 x^{3}

= 6 - 12 x + 6 x^{2} - 4 + 12 x - 12 x^{2} + 4 x^{3} - 6 x + 12 x^{2} - 6 x^{3} - 1

簡素化

6 - 12 x + 6 x^{2} - 4 + 12 x - 12 x^{2} + 4 x^{3} - 6 x + 12 x^{2} - 6 x^{3} - 1 : - 2 x^{3} + 6 x^{2} - 6 x + 1

= - 2 x^{3} + 6 x^{2} - 6 x + 1