因数 9-12cos(4x)+4cos^2(4x)

解

因数

9 - 12 cos (4 x) + 4 cos^{2} (4 x)

(2 cos (4 x) - 3)^{2}

解答ステップ

9 - 12 cos (4 x) + 4 cos^{2} (4 x)

標準的な形式で書く

a x^{2} + b x + c

= 4 cos^{2} (4 x) - 12 cos (4 x) + 9

4 cos^{2} (4 x) - 12 cos (4 x) + 9

を書き換え

(2 cos (4 x))^{2} - 2 \cdot 2 cos (4 x) \cdot 3 + 3^{2}

= (2 cos (4 x))^{2} - 2 \cdot 2 cos (4 x) \cdot 3 + 3^{2}

完全平方式を適用する:

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

a = 2 cos (4 x), b = 3

= (2 cos (4 x) - 3)^{2}