Square of a Sum

For any two numbers a and b,

(((a+b))^2)=(a^2)+2a b+(b^2).

In words, the square of a sum is the sum of the squares plus twice the cross term.

You can see a geometrical proof of this identity from the figure above. The gray numbers represent the side lengths or areas of the entire figure and the black ones represent the side lengths or areas of the colored regions. Each set of numbers on the sides or in the middle of the figure sums to the gray number.

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Contributed by: Joe Bolte

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