展開する (tan(x)-4)(tan(x)+4)(tan(x)-2)(tan(x)+2)

解

展開する

(tan (x) - 4) (tan (x) + 4) (tan (x) - 2) (tan (x) + 2)

tan^{4} (x) - 20 tan^{2} (x) + 64

解答ステップ

(tan (x) - 4) (tan (x) + 4) (tan (x) - 2) (tan (x) + 2)

拡張

(tan (x) - 4) (tan (x) + 4) (tan (x) - 2) (tan (x) + 2) : (tan^{2} (x) - 16) (tan (x) - 2) (tan (x) + 2)

= (tan^{2} (x) - 16) (tan (x) - 2) (tan (x) + 2)

2つの正方形の差

(tan (x) - 2) (tan (x) + 2) を適用します : tan^{2} (x) - 4

= (tan^{2} (x) - 16) (tan^{2} (x) - 4)

FOIL方法

(tan^{2} (x) - 16) (tan^{2} (x) - 4)

を適用します:

tan^{4} (x) - 20 tan^{2} (x) + 64

= tan^{4} (x) - 20 tan^{2} (x) + 64