簡約 (((a-b)^2+(b-c)^2+(a-c)^2))/(12)

解

簡約

\frac{( ( a - b ) ^{2} + ( b - c ) ^{2} + ( a - c ) ^{2} )}{12}

\frac{a ^{2} - ab + b ^{2} - b c + c ^{2} - a c}{6}

解答ステップ

\frac{( a - b ) ^{2} + ( b - c ) ^{2} + ( a - c ) ^{2}}{12}

拡張

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

= \frac{2 a ^{2} - 2 ab + 2 b ^{2} - 2 b c + 2 c ^{2} - 2 a c}{12}

共通項をくくり出す

2

= \frac{2 ( a ^{2} - ab + b ^{2} - b c + c ^{2} - a c )}{12}

数を因数に分解する:

12 = 2 \cdot 6

= \frac{2 ( a ^{2} - ab + b ^{2} - b c + c ^{2} - a c )}{2 \cdot 6}

共通因数を約分する:

2

= \frac{a ^{2} - ab + b ^{2} - b c + c ^{2} - a c}{6}