展開する (x-9)(x-3)^2ln(x/6)

解

展開する

(x - 9) (x - 3)^{2} ln (\frac{x}{6})

x^{3} ln (\frac{x}{6}) - 15 x^{2} ln (\frac{x}{6}) + 63 x ln (\frac{x}{6}) - 81 ln (\frac{x}{6})

解答ステップ

(x - 9) (x - 3)^{2} ln (\frac{x}{6})

= ln (\frac{x}{6}) (x - 9) (x - 3)^{2}

分配法則を適用する:

a (b - c) = ab - a c

a = (x - 3)^{2} ln (\frac{x}{6}), b = x, c = 9

= (x - 3)^{2} ln (\frac{x}{6}) x - (x - 3)^{2} ln (\frac{x}{6}) \cdot 9

= x ln (\frac{x}{6}) (x - 3)^{2} - 9 ln (\frac{x}{6}) (x - 3)^{2}

簡素化

x ln (\frac{x}{6}) (x - 3)^{2} - 9 ln (\frac{x}{6}) (x - 3)^{2} : x^{3} ln (\frac{x}{6}) - 15 x^{2} ln (\frac{x}{6}) + 63 x ln (\frac{x}{6}) - 81 ln (\frac{x}{6})

= x^{3} ln (\frac{x}{6}) - 15 x^{2} ln (\frac{x}{6}) + 63 x ln (\frac{x}{6}) - 81 ln (\frac{x}{6})