展開する (x-a)(x-b)(x-c)(x-d)

解

展開する

(x - a) (x - b) (x - c) (x - d)

x^{4} - x^{3} d - x^{3} c + x^{2} c d - x^{3} b + x^{2} b d + x^{2} b c - b c d x - a x^{3} + a x^{2} d + a x^{2} c - a c d x + a x^{2} b - ab d x - ab c x + ab c d

解答ステップ

(x - a) (x - b) (x - c) (x - d)

拡張

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

= (x^{2} - b x - a x + ab) (x - c) (x - d)

FOIL方法

(x - c) (x - d)

を適用します:

x^{2} - d x - c x + c d

= (x^{2} - b x - a x + ab) (x^{2} - d x - c x + c d)

括弧を分配する

= x^{2} x^{2} + x^{2} (- d x) + x^{2} (- c x) + x^{2} c d - b x x^{2} - b x (- d x) - b x (- c x) - b x c d - a x x^{2} - a x (- d x) - a x (- c x) - a x c d + ab x^{2} + ab (- d x) + ab (- c x) + ab c d

簡素化

x^{2} x^{2} + x^{2} (- d x) + x^{2} (- c x) + x^{2} c d - b x x^{2} - b x (- d x) - b x (- c x) - b x c d - a x x^{2} - a x (- d x) - a x (- c x) - a x c d + ab x^{2} + ab (- d x) + ab (- c x) + ab c d : x^{4} - x^{3} d - x^{3} c + x^{2} c d - x^{3} b + x^{2} b d + x^{2} b c - b c d x - a x^{3} + a x^{2} d + a x^{2} c - a c d x + a x^{2} b - ab d x - ab c x + ab c d

= x^{4} - x^{3} d - x^{3} c + x^{2} c d - x^{3} b + x^{2} b d + x^{2} b c - b c d x - a x^{3} + a x^{2} d + a x^{2} c - a c d x + a x^{2} b - ab d x - ab c x + ab c d