What is expand (L-t/2)(r)(H+k/2)^2 ?

The solution to expand (L-t/2)(r)(H+k/2)^2 is H^2Lr+LHkr+(Lk^2r)/4-(H^2tr)/2-(Hktr)/2-(k^2tr)/8

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

expand

(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}

Solution steps

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

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

Apply the distributive law:

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}

Simplify

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}

\frac{1}{s ( s + 1 ) ( s ^{2} + 6 s + 13 )}

\frac{x x ^{2} + 36 \cdot 3 - 2 ( x ^{2} + 36 )}{6 ( x ^{2} + 36 )}

ln (4) m^{3} n^{5}

\frac{( x ^{2} - 2 x + 1 )}{x ^{2} ( 2 x ^{2} + 1 )}

\frac{u ^{5} ( u ^{3} + 1 )}{u ^{2} + 1}

What is expand (L-t/2)(r)(H+k/2)^2 ?
The solution to expand (L-t/2)(r)(H+k/2)^2 is H^2Lr+LHkr+(Lk^2r)/4-(H^2tr)/2-(Hktr)/2-(k^2tr)/8