因数 (a+b+c)(ab+ac+bc)-abc

解

因数

(a + b + c) (ab + a c + b c) - ab c

a^{2} b + a^{2} c + a b^{2} + a c^{2} + 2 ab c + b c^{2} + b^{2} c

解答ステップ

(a + b + c) (ab + a c + b c) - ab c

拡張

(a + b + c) (ab + a c + b c) : a^{2} b + a b^{2} + a^{2} c + 3 ab c + a c^{2} + b^{2} c + b c^{2}

= a^{2} b + a b^{2} + a^{2} c + 3 ab c + a c^{2} + b^{2} c + b c^{2} - ab c

簡素化

a^{2} b + a b^{2} + a^{2} c + 3 ab c + a c^{2} + b^{2} c + b c^{2} - ab c : a^{2} b + a^{2} c + a b^{2} + a c^{2} + 2 ab c + b c^{2} + b^{2} c

= a^{2} b + a^{2} c + a b^{2} + a c^{2} + 2 ab c + b c^{2} + b^{2} c