ABC26GN0176 · Number System

$$\begin{aligned} (107 \times 107)+(93 \times 93) & =(107)^{2}+(93)^{2} \\ & =(100+7)^{2}+(100-7)^{2} \\ & =(a+b)^{2}+(a-b)^{2}=2\left(a^{2}+b^{2}\right) \\ & =2\left[(100)^{2}+7^{2}\right]=2[10000+49] \\ & =2 \times 10049=20098 . \end{aligned}$$