Squaring numbers

Algebra Level 2

Numbers could be squared using the following algorithm:

\[\large {41 \times 41=\color{blue}40 \times \color{red}42 + \color{purple}1^2=\color{green}1681 \\ 32 \times 32=\color{blue}30 \times \color{red}34 + \color{purple}2^2=\color{green}1024 \\ 57 \times 57=\color{blue}54 \times \color{red}60 + \color{purple}3^2=\color{green}3249 \\ 89 \times 89=\color{blue}88 \times \color{red}90 +\color{purple}1^2=\color{green}7921 \\ \vdots }\]

Find \(78 \times 78\)

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