簡約 (2x+3)^2-(x-5)^2

解

簡約

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

3 x^{2} + 22 x - 16

解答ステップ

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

拡張

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

= 4 x^{2} + 12 x + 9 - (x - 5)^{2}

拡張

- (x - 5)^{2} : - x^{2} + 10 x - 25

= 4 x^{2} + 12 x + 9 - x^{2} + 10 x - 25

条件のようなグループ

= 4 x^{2} - x^{2} + 12 x + 10 x + 9 - 25

類似した元を足す:

4 x^{2} - x^{2} = 3 x^{2}

= 3 x^{2} + 12 x + 10 x + 9 - 25

類似した元を足す:

12 x + 10 x = 22 x

= 3 x^{2} + 22 x + 9 - 25

数を引く:

9 - 25 = - 16

= 3 x^{2} + 22 x - 16