\[a^2 \times 10^{2x} + 2(ab \times 10^x) + b^2 \\ = (a \times 10^x + b)^2 = \overline{a \underbrace{00 \dots 00}_{x - 1个0} b}^2 \\ = \overline{x \underbrace{00 \dots 00}_{x - 1个0}z \underbrace{00 \dots 00}_{x - 1个0}y}(x = a^2,y = b^2,z = 2ab)\]

\[a^2 \times 10^{2x + 1} + 2(ab \times 10^{2x + 1}) + b^2 \times 10^{2x} \\ = (a^2 \times 10^2 + 2ab \times 10 + b ^ 2) \times 10^{2x} \\ = (a \times 10 + b)^2 \times 10^{x^2} \\ = \overline{ab}^2 \times 10^{x^2} = \overline{ab \underbrace{00 \dots 00}_{x个0}}^2 \\ = \overline{xzy \underbrace{00 \dots 00}_{x个0}}(x = a^2,y = b^2,z = 2ab)\]

\[x,y,z\in (0,10)\]