簡約 (x+3)(x^2-3x+9)-(x-1)^3+3(x^2-1)

解

簡約

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

6 x^{2} - 3 x + 25

解答ステップ

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

拡張

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

= x^{3} + 27 - (x - 1)^{3} + 3 (x^{2} - 1)

拡張

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

= x^{3} + 27 - x^{3} + 3 x^{2} - 3 x + 1 + 3 (x^{2} - 1)

拡張

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

= x^{3} + 27 - x^{3} + 3 x^{2} - 3 x + 1 + 3 x^{2} - 3

条件のようなグループ

= x^{3} - x^{3} + 3 x^{2} + 3 x^{2} - 3 x + 27 + 1 - 3

類似した元を足す:

x^{3} - x^{3} = 0

= 3 x^{2} + 3 x^{2} - 3 x + 27 + 1 - 3

類似した元を足す:

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

= 6 x^{2} - 3 x + 27 + 1 - 3

数を足す:

27 + 1 - 3 = 25

= 6 x^{2} - 3 x + 25