展開する (4-cos^2(t))^2

解

展開する

(4 - cos^{2} (t))^{2}

16 - 8 cos^{2} (t) + cos^{4} (t)

解答ステップ

(4 - cos^{2} (t))^{2}

完全平方式を適用する:

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

(4 - cos^{2} (t))^{2} = 4^{2} - 2 \cdot 4 cos^{2} (t) + (cos^{2} (t))^{2}

= 4^{2} - 2 \cdot 4 cos^{2} (t) + (cos^{2} (t))^{2}

簡素化

4^{2} - 2 \cdot 4 cos^{2} (t) + (cos^{2} (t))^{2} : 16 - 8 cos^{2} (t) + cos^{4} (t)

= 16 - 8 cos^{2} (t) + cos^{4} (t)