Explain the Pattern - Part 2

Algebra Level 1

\[ \large \begin{align} 51 \times 51 &= {\color{blue}26}{\color{red}01} \\ 52 \times 52 &= {\color{blue}27}{\color{red}04} \\ 53 \times 53 &= {\color{blue}28}{\color{red}09} \\ 54 \times 54 &= {\color{blue}29}{\color{red}16} \\ 55 \times 55 &= {\color{blue}30}{\color{red}25} \\ 56 \times 56 &= {\color{blue}31}{\color{red}36} \\ & \vdots \end{align} \]

What is the value of \( 57 \times 57?\)


Bonus: Can you explain why this pattern appears, and when it breaks?

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