展開する (a+b*cos(t))^3

解

展開する

(a + b \cdot cos (t))^{3}

a^{3} + 3 a^{2} b cos (t) + 3 a b^{2} cos^{2} (t) + b^{3} cos^{3} (t)

解答ステップ

(a + b cos (t))^{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}

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

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

簡素化

a^{3} + 3 a^{2} b cos (t) + 3 a (b cos (t))^{2} + (b cos (t))^{3} : a^{3} + 3 a^{2} b cos (t) + 3 a b^{2} cos^{2} (t) + b^{3} cos^{3} (t)

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