erweitern (L-t/2)(r)(H+k/2)^2

Lösung

erweitern

(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}

Schritte zur Lösung

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

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

Wende das Distributivgesetz an:

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}

Vereinfache

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}

e x p an d \frac{1}{s ( s + 1 ) ( s ^{2} + 6 s + 13 )}

s im pl i f y \frac{x x ^{2} + 36 \cdot 3 - 2 ( x ^{2} + 36 )}{6 ( x ^{2} + 36 )}

e x p an d ln (4) m^{3} n^{5}

e x p an d \frac{( x ^{2} - 2 x + 1 )}{x ^{2} ( 2 x ^{2} + 1 )}

e x p an d \frac{u ^{5} ( u ^{3} + 1 )}{u ^{2} + 1}