展開する (L-t/2)(r)(H+k/2)^2

解

展開する

(L - \frac{t}{2}) (r) (H + \frac{k}{2})^{2}

H^{2} L r + L H k r + \frac{L k ^{2} r}{4} - \frac{H ^{2} t r}{2} - \frac{H k t r}{2} - \frac{k ^{2} t r}{8}

解答ステップ

(L - \frac{t}{2}) (r) (H + \frac{k}{2})^{2}

= (r) (L - \frac{t}{2}) (H + \frac{k}{2})^{2}

分配法則を適用する:

a (b - c) = ab - a c

a = (r) (H + \frac{k}{2})^{2}, b = L, c = \frac{t}{2}

= (r) (H + \frac{k}{2})^{2} L - (r) (H + \frac{k}{2})^{2} \frac{t}{2}

= L (r) (H + \frac{k}{2})^{2} - \frac{t}{2} (r) (H + \frac{k}{2})^{2}

簡素化

L (r) (H + \frac{k}{2})^{2} - \frac{t}{2} (r) (H + \frac{k}{2})^{2} : H^{2} L r + L H k r + \frac{L k ^{2} r}{4} - \frac{H ^{2} t r}{2} - \frac{H k t r}{2} - \frac{k ^{2} t r}{8}

= H^{2} L r + L H k r + \frac{L k ^{2} r}{4} - \frac{H ^{2} t r}{2} - \frac{H k t r}{2} - \frac{k ^{2} t r}{8}