簡約 (3x+1)^2-2(3x+1)(3x+5)+(3x+5)^2

解

簡約

(3 x + 1)^{2} - 2 (3 x + 1) (3 x + 5) + (3 x + 5)^{2}

16

解答ステップ

(3 x + 1)^{2} - 2 (3 x + 1) (3 x + 5) + (3 x + 5)^{2}

拡張

(3 x + 1)^{2} : 9 x^{2} + 6 x + 1

= 9 x^{2} + 6 x + 1 - 2 (3 x + 1) (3 x + 5) + (3 x + 5)^{2}

拡張

- 2 (3 x + 1) (3 x + 5) : - 18 x^{2} - 36 x - 10

= 9 x^{2} + 6 x + 1 - 18 x^{2} - 36 x - 10 + (3 x + 5)^{2}

拡張

(3 x + 5)^{2} : 9 x^{2} + 30 x + 25

= 9 x^{2} + 6 x + 1 - 18 x^{2} - 36 x - 10 + 9 x^{2} + 30 x + 25

条件のようなグループ

= 9 x^{2} - 18 x^{2} + 9 x^{2} + 6 x - 36 x + 30 x + 1 - 10 + 25

類似した元を足す:

9 x^{2} - 18 x^{2} + 9 x^{2} = 0

= 6 x - 36 x + 30 x + 1 - 10 + 25

類似した元を足す:

6 x - 36 x + 30 x = 0

= 1 - 10 + 25

数を足す:

1 - 10 + 25 = 16

= 16