簡約 (2x+3)^2-(2x-3)^2+(3x-4)^2-8x^2-16

解

簡約

(2 x + 3)^{2} - (2 x - 3)^{2} + (3 x - 4)^{2} - 8 x^{2} - 16

x^{2}

解答ステップ

(2 x + 3)^{2} - (2 x - 3)^{2} + (3 x - 4)^{2} - 8 x^{2} - 16

拡張

(2 x + 3)^{2} : 4 x^{2} + 12 x + 9

= 4 x^{2} + 12 x + 9 - (2 x - 3)^{2} + (3 x - 4)^{2} - 8 x^{2} - 16

拡張

- (2 x - 3)^{2} : - 4 x^{2} + 12 x - 9

= 4 x^{2} + 12 x + 9 - 4 x^{2} + 12 x - 9 + (3 x - 4)^{2} - 8 x^{2} - 16

拡張

(3 x - 4)^{2} : 9 x^{2} - 24 x + 16

= 4 x^{2} + 12 x + 9 - 4 x^{2} + 12 x - 9 + 9 x^{2} - 24 x + 16 - 8 x^{2} - 16

条件のようなグループ

= 4 x^{2} - 4 x^{2} + 9 x^{2} - 8 x^{2} + 12 x + 12 x - 24 x + 9 - 9 + 16 - 16

類似した元を足す:

4 x^{2} - 4 x^{2} + 9 x^{2} - 8 x^{2} = x^{2}

= x^{2} + 12 x + 12 x - 24 x + 9 - 9 + 16 - 16

類似した元を足す:

12 x + 12 x - 24 x = 0

= x^{2} + 9 - 9 + 16 - 16

数を足す:

9 - 9 + 16 - 16 = 0

= x^{2}