展開する (4(x+tan(x))^3)× (1+sec^2(x))

解

展開する

(4 (x + tan (x))^{3}) \cdot (1 + sec^{2} (x))

4 x^{3} + 12 x^{2} tan (x) + 12 x tan^{2} (x) + 4 tan^{3} (x) + 4 sec^{2} (x) x^{3} + 12 sec^{2} (x) x^{2} tan (x) + 12 x sec^{2} (x) tan^{2} (x) + 4 sec^{2} (x) tan^{3} (x)

解答ステップ

(4 (x + tan (x))^{3}) (1 + sec^{2} (x))

分配法則を適用する:

a (b + c) = ab + a c

(4 (x + tan (x))^{3}) (1 + sec^{2} (x)) = 4 (x + tan (x))^{3} \cdot 1 + 4 (x + tan (x))^{3} sec^{2} (x)

= 4 (x + tan (x))^{3} \cdot 1 + 4 (x + tan (x))^{3} sec^{2} (x)

簡素化

4 (x + tan (x))^{3} \cdot 1 + 4 (x + tan (x))^{3} sec^{2} (x) : 4 (x + tan (x))^{3} + 4 sec^{2} (x) (x + tan (x))^{3}

= 4 (x + tan (x))^{3} + 4 sec^{2} (x) (x + tan (x))^{3}

拡張

4 (x + tan (x))^{3} : 4 x^{3} + 12 x^{2} tan (x) + 12 x tan^{2} (x) + 4 tan^{3} (x)

= 4 x^{3} + 12 x^{2} tan (x) + 12 x tan^{2} (x) + 4 tan^{3} (x) + 4 sec^{2} (x) (x + tan (x))^{3}

拡張

4 sec^{2} (x) (x + tan (x))^{3} : 4 sec^{2} (x) x^{3} + 12 sec^{2} (x) x^{2} tan (x) + 12 x sec^{2} (x) tan^{2} (x) + 4 sec^{2} (x) tan^{3} (x)

= 4 x^{3} + 12 x^{2} tan (x) + 12 x tan^{2} (x) + 4 tan^{3} (x) + 4 sec^{2} (x) x^{3} + 12 sec^{2} (x) x^{2} tan (x) + 12 x sec^{2} (x) tan^{2} (x) + 4 sec^{2} (x) tan^{3} (x)