I just showed my 5 yo how if you know 4^2 = 16, you can say how many balls are in a 4 x 4 square without counting them all.
The area of this new almost-square is 4 times the product of the two unknown numbers. Its side length is their sum.
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The crucial final point is that the side length of the missing square at its center is the difference between the two unknown numbers.
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The sum of these unknown numbers is known, so its square is as well. And this is 4 times their product, plus the square of their difference.
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