簡約 ((x-3)^1)^3+((x-3^2)^1)^3

解

簡約

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

2 x^{3} - 36 x^{2} + 270 x - 756

解答ステップ

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

((x - 3)^{1})^{3} = (x - 3)^{3}

((x - 3^{2})^{1})^{3} = (x - 9)^{3}

= (x - 3)^{3} + (x - 9)^{3}

拡張

(x - 3)^{3} : x^{3} - 9 x^{2} + 27 x - 27

= x^{3} - 9 x^{2} + 27 x - 27 + (x - 9)^{3}

拡張

(x - 9)^{3} : x^{3} - 27 x^{2} + 243 x - 729

= x^{3} - 9 x^{2} + 27 x - 27 + x^{3} - 27 x^{2} + 243 x - 729

条件のようなグループ

= x^{3} + x^{3} - 9 x^{2} - 27 x^{2} + 27 x + 243 x - 27 - 729

類似した元を足す:

x^{3} + x^{3} = 2 x^{3}

= 2 x^{3} - 9 x^{2} - 27 x^{2} + 27 x + 243 x - 27 - 729

類似した元を足す:

- 9 x^{2} - 27 x^{2} = - 36 x^{2}

= 2 x^{3} - 36 x^{2} + 27 x + 243 x - 27 - 729

類似した元を足す:

27 x + 243 x = 270 x

= 2 x^{3} - 36 x^{2} + 270 x - 27 - 729

数を引く:

- 27 - 729 = - 756

= 2 x^{3} - 36 x^{2} + 270 x - 756