展開する (1-pcos(x)+xp*cos(x))^2

解

展開する

(1 - p \cdot cos (x) + x \cdot p \cdot cos (x))^{2}

- 2 p cos (x) + p^{2} cos^{2} (x) + 2 p x cos (x) - 2 p^{2} x cos^{2} (x) + x^{2} p^{2} cos^{2} (x) + 1

解答ステップ

(1 - p cos (x) + x p cos (x))^{2}

指数の規則を適用する:

a^{b + c} = a^{b} \cdot a^{c}

(1 - p cos (x) + x p cos (x))^{2} = (1 - p cos (x) + x p cos (x)) (1 - p cos (x) + x p cos (x))

= (1 - p cos (x) + x p cos (x)) (1 - p cos (x) + x p cos (x))

括弧を分配する

= 1 \cdot 1 + 1 \cdot (- p cos (x)) + 1 \cdot x p cos (x) - p cos (x) \cdot 1 - p cos (x) (- p cos (x)) - p cos (x) x p cos (x) + x p cos (x) \cdot 1 + x p cos (x) (- p cos (x)) + x p cos (x) x p cos (x)

簡素化

1 \cdot 1 + 1 \cdot (- p cos (x)) + 1 \cdot x p cos (x) - p cos (x) \cdot 1 - p cos (x) (- p cos (x)) - p cos (x) x p cos (x) + x p cos (x) \cdot 1 + x p cos (x) (- p cos (x)) + x p cos (x) x p cos (x) : - 2 p cos (x) + p^{2} cos^{2} (x) + 2 p x cos (x) - 2 p^{2} x cos^{2} (x) + x^{2} p^{2} cos^{2} (x) + 1

= - 2 p cos (x) + p^{2} cos^{2} (x) + 2 p x cos (x) - 2 p^{2} x cos^{2} (x) + x^{2} p^{2} cos^{2} (x) + 1