$$U_{710}(x, y) = 2 x y^{2} + 4 x y + 2 x + \left(y + 1\right) \sqrt{4 x^{2} y^{2} + 8 x^{2} y + 4 x^{2} + 1}$$

$$Tsqrt(n, k) = \begin{cases}\binom{m}{n} 4^{n}&\text{if k even, where m =} \frac{k} {2},\\\frac {{(-1)}^{n-m} \binom{n}{m} \binom{2n}{n}} {\binom{2n}{2m}} &\text{if k odd, n > m, where m =} \frac{k+1} {2},\\\frac {\binom{2m}{2n} \binom{2n}{n}} {\binom{m}{n}}&\text{if k odd, n} \le \text{m, where m =} \frac{k+1} {2},\\\end{cases} $$$$T_{710}(n, m, k) = \frac{k \operatorname{Tsqrt}{\left(n,k + n \right)} {\binom{k + n}{m}}}{k + n}$$