展開する (1+cos^2(7x))^3

解

展開する

(1 + cos^{2} (7 x))^{3}

1 + 3 cos^{2} (7 x) + 3 cos^{4} (7 x) + cos^{6} (7 x)

解答ステップ

(1 + cos^{2} (7 x))^{3}

完全立方式を適用する:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

(1 + cos^{2} (7 x))^{3} = 1^{3} + 3 \cdot 1^{2} cos^{2} (7 x) + 3 \cdot 1 \cdot (cos^{2} (7 x))^{2} + (cos^{2} (7 x))^{3}

= 1^{3} + 3 \cdot 1^{2} cos^{2} (7 x) + 3 \cdot 1 \cdot (cos^{2} (7 x))^{2} + (cos^{2} (7 x))^{3}

簡素化

1^{3} + 3 \cdot 1^{2} cos^{2} (7 x) + 3 \cdot 1 \cdot (cos^{2} (7 x))^{2} + (cos^{2} (7 x))^{3} : 1 + 3 cos^{2} (7 x) + 3 cos^{4} (7 x) + cos^{6} (7 x)

= 1 + 3 cos^{2} (7 x) + 3 cos^{4} (7 x) + cos^{6} (7 x)