The simplified value of ( 6 + 10 - 21 - 35 ) ( 6 - 10 + 21 - 35 ) is

Answer: Option D

$$\begin{array}{rl}& \left(\sqrt{6}+\sqrt{10}-\sqrt{21}-\sqrt{35}\right)\left(\sqrt{6}-\sqrt{10}+\sqrt{21}-\sqrt{35}\right)\\ & =\left\{\left(\sqrt{6}-\sqrt{35}\right)+\left(\sqrt{10}-\sqrt{21}\right)\right\}\left\{\left(\sqrt{6}-\sqrt{35}\right)-\left(\sqrt{10}-\sqrt{21}\right)\right\}\\ & ={\left(\sqrt{6}-\sqrt{35}\right)}^2-{\left(\sqrt{10}-\sqrt{21}\right)}^2\\ & =\left(6-35-2\sqrt{210}\right)-\left(10+21-2\sqrt{210}\right)\\ & =41-2\sqrt{210}-31+2\sqrt{210}\\ & =41-31\\ & =10\end{array}$$