展開する (2a+b+c)^3

解

展開する

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

8 a^{3} + 12 a^{2} b + 12 a^{2} c + 3 b^{2} c + 3 b c^{2} + 6 a b^{2} + 6 a c^{2} + 12 ab c + b^{3} + c^{3}

解答ステップ

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

簡素化

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

= (2 a + b + c) (2 a + b + c) (2 a + b + c)

拡張

(2 a + b + c) (2 a + b + c) : 4 a^{2} + 2 b c + 4 ab + 4 a c + b^{2} + c^{2}

= (4 a^{2} + 2 b c + 4 ab + 4 a c + b^{2} + c^{2}) (2 a + b + c)

括弧を分配する

= 4 a^{2} \cdot 2 a + 4 a^{2} b + 4 a^{2} c + 2 b c \cdot 2 a + 2 b c b + 2 b cc + 4 ab \cdot 2 a + 4 abb + 4 ab c + 4 a c \cdot 2 a + 4 a c b + 4 a cc + b^{2} \cdot 2 a + b^{2} b + b^{2} c + c^{2} \cdot 2 a + c^{2} b + c^{2} c

簡素化

4 a^{2} \cdot 2 a + 4 a^{2} b + 4 a^{2} c + 2 b c \cdot 2 a + 2 b c b + 2 b cc + 4 ab \cdot 2 a + 4 abb + 4 ab c + 4 a c \cdot 2 a + 4 a c b + 4 a cc + b^{2} \cdot 2 a + b^{2} b + b^{2} c + c^{2} \cdot 2 a + c^{2} b + c^{2} c : 8 a^{3} + 12 a^{2} b + 12 a^{2} c + 3 b^{2} c + 3 b c^{2} + 6 a b^{2} + 6 a c^{2} + 12 ab c + b^{3} + c^{3}

= 8 a^{3} + 12 a^{2} b + 12 a^{2} c + 3 b^{2} c + 3 b c^{2} + 6 a b^{2} + 6 a c^{2} + 12 ab c + b^{3} + c^{3}