What is (sqrt(L)+2sqrt(K))^2*K^{(1/2)} ?

The solution to (sqrt(L)+2sqrt(K))^2*K^{(1/2)} is K^{1/2}(L+4sqrt(L)sqrt(K)+4K)

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simplify (sqrt(L)+2sqrt(K))^2*K^{(1/2)}

simplify

(L + 2 K)^{2} \cdot K^{(\frac{1}{2})}

K^{\frac{1}{2}} (L + 4 L K + 4 K)

Solution steps

(L + 2 K)^{2} K^{\frac{1}{2}}

Expand

(L + 2 K)^{2} : L + 4 L K + 4 K

= (L + 4 L K + 4 K) K^{\frac{1}{2}}

= K^{\frac{1}{2}} (L + 4 L K + 4 K)

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

- \frac{16 ( 8 - 3 x ^{2} )}{( x ^{2} + 8 ) ^{3}}

\frac{( 1 + x )}{( 1 - x ) ^{3}}

\frac{21937.5}{20000}

\frac{k ( k - 1 ) ( k + 1 )}{3}

What is (sqrt(L)+2sqrt(K))^2*K^{(1/2)} ?
The solution to (sqrt(L)+2sqrt(K))^2*K^{(1/2)} is K^{1/2}(L+4sqrt(L)sqrt(K)+4K)