簡約 (2a-c)^2-(a+c)^2

解

簡約

(2 a - c)^{2} - (a + c)^{2}

3 a^{2} - 6 a c

解答ステップ

(2 a - c)^{2} - (a + c)^{2}

拡張

(2 a - c)^{2} : 4 a^{2} - 4 a c + c^{2}

= 4 a^{2} - 4 a c + c^{2} - (a + c)^{2}

拡張

- (a + c)^{2} : - a^{2} - 2 a c - c^{2}

= 4 a^{2} - 4 a c + c^{2} - a^{2} - 2 a c - c^{2}

条件のようなグループ

= 4 a^{2} - a^{2} + c^{2} - c^{2} - 4 a c - 2 a c

類似した元を足す:

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

= 3 a^{2} + c^{2} - c^{2} - 4 a c - 2 a c

類似した元を足す:

c^{2} - c^{2} = 0

= 3 a^{2} - 4 a c - 2 a c

類似した元を足す:

- 4 a c - 2 a c = - 6 a c

= 3 a^{2} - 6 a c