jmc

We can start by pairing the terms in this expression and factoring them as a difference of squares: $$\begin{array}{rl}& (19^2-17^2)+(15^2-13^2)+(11^2-9^2)+(7^2-5^2)+(3^2-1^2)\\ & =2(19+17)+2(15+13)+2(11+9)+2(7+5)+2(3+1)\\ & =2(19+17+15+13+11+9+7+5+3+1)\\ & =2(100)\\ & =\boxed{200}.\end{array}$$