簡約 (2x+1)^2+(3x-1)^2+2(2x+1)(3x-1)

解

簡約

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

25 x^{2}

解答ステップ

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

拡張

(2 x + 1)^{2} : 4 x^{2} + 4 x + 1

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

拡張

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

= 4 x^{2} + 4 x + 1 + 9 x^{2} - 6 x + 1 + 2 (2 x + 1) (3 x - 1)

拡張

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

= 4 x^{2} + 4 x + 1 + 9 x^{2} - 6 x + 1 + 12 x^{2} + 2 x - 2

条件のようなグループ

= 4 x^{2} + 9 x^{2} + 12 x^{2} + 4 x - 6 x + 2 x + 1 + 1 - 2

類似した元を足す:

4 x^{2} + 9 x^{2} + 12 x^{2} = 25 x^{2}

= 25 x^{2} + 4 x - 6 x + 2 x + 1 + 1 - 2

類似した元を足す:

4 x - 6 x + 2 x = 0

= 25 x^{2} + 1 + 1 - 2

数を足す:

1 + 1 - 2 = 0

= 25 x^{2}