簡約 x(ax-1)(ax-a-1)(x+1)+a

解

簡約

x (a x - 1) (a x - a - 1) (x + 1) + a

x^{4} a^{2} - 2 a x^{3} - x^{2} a^{2} + x^{2} - a x^{2} + a x + x + a

解答ステップ

x (a x - 1) (a x - a - 1) (x + 1) + a

FOIL方法

(a x - 1) (x + 1)

を適用します:

a x^{2} + a x - x - 1

= x (a x^{2} + a x - x - 1) (a x - a - 1) + a

拡張

(a x^{2} + a x - x - 1) (a x - a - 1) : a^{2} x^{3} - 2 a x^{2} - x a^{2} + x - a x + a + 1

= x (a^{2} x^{3} - 2 a x^{2} - x a^{2} + x - a x + a + 1) + a

括弧を分配する

= x a^{2} x^{3} + x (- 2 a x^{2}) + x (- x a^{2}) + xx + x (- a x) + x a + x \cdot 1 + a

簡素化

x a^{2} x^{3} + x (- 2 a x^{2}) + x (- x a^{2}) + xx + x (- a x) + x a + x \cdot 1 : x^{4} a^{2} - 2 a x^{3} - x^{2} a^{2} + x^{2} - a x^{2} + a x + x

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