展開する (t-1)^2(\H(t-1)-\H(t-2))

解

展開する

(t - 1)^{2} (H (t - 1) - H (t - 2))

t^{2} H (t - 1) - 2 t H (t - 1) + H (t - 1) - t^{2} H (t - 2) + 2 t H (t - 2) - H (t - 2)

解答ステップ

(t - 1)^{2} (H (t - 1) - H (t - 2))

分配法則を適用する:

a (b - c) = ab - a c

a = (t - 1)^{2}, b = H (t - 1), c = H (t - 2)

= (t - 1)^{2} H (t - 1) - (t - 1)^{2} H (t - 2)

= H (t - 1) (t - 1)^{2} - H (t - 2) (t - 1)^{2}

簡素化

H (t - 1) (t - 1)^{2} - H (t - 2) (t - 1)^{2} : t^{2} H (t - 1) - 2 t H (t - 1) + H (t - 1) - t^{2} H (t - 2) + 2 t H (t - 2) - H (t - 2)

= t^{2} H (t - 1) - 2 t H (t - 1) + H (t - 1) - t^{2} H (t - 2) + 2 t H (t - 2) - H (t - 2)