Explain the Pattern - Part 2

Algebra Level 1

51×51=260152×52=270453×53=280954×54=291655×55=302556×56=3136 \large \begin{aligned} 51 \times 51 &= {\color{#3D99F6}26}{\color{#D61F06}01} \\ 52 \times 52 &= {\color{#3D99F6}27}{\color{#D61F06}04} \\ 53 \times 53 &= {\color{#3D99F6}28}{\color{#D61F06}09} \\ 54 \times 54 &= {\color{#3D99F6}29}{\color{#D61F06}16} \\ 55 \times 55 &= {\color{#3D99F6}30}{\color{#D61F06}25} \\ 56 \times 56 &= {\color{#3D99F6}31}{\color{#D61F06}36} \\ & \vdots \end{aligned}

What is the value of 57×57? 57 \times 57?


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

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