簡約 a(a+1)(a+2)(a+3)-15

解

簡約

a (a + 1) (a + 2) (a + 3) - 15

a^{4} + 6 a^{3} + 11 a^{2} + 6 a - 15

解答ステップ

a (a + 1) (a + 2) (a + 3) - 15

FOIL方法

(a + 1) (a + 2)

を適用します:

a^{2} + 3 a + 2

= a (a^{2} + 3 a + 2) (a + 3) - 15

拡張

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

= (a^{2} + 3 a) (a^{2} + 3 a + 2) - 15

括弧を分配する

= a^{2} a^{2} + a^{2} \cdot 3 a + a^{2} \cdot 2 + 3 a a^{2} + 3 a \cdot 3 a + 3 a \cdot 2 - 15

簡素化

a^{2} a^{2} + a^{2} \cdot 3 a + a^{2} \cdot 2 + 3 a a^{2} + 3 a \cdot 3 a + 3 a \cdot 2 : a^{4} + 6 a^{3} + 11 a^{2} + 6 a

= a^{4} + 6 a^{3} + 11 a^{2} + 6 a - 15