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Why the square of the sum of two numbers is different from the sum of the squares of two numbers?
Wiki User
∙ 12y ago
call the numbers a & b
(a+b)2 = a2+2ab+b2
which is greater than a2 + b2 by twice the product of the numbers.
Check: say 3 and 5
32 + 52 = 9 + 25 = 34
(3 +5)2 = 64, greater by twice a x b. QED
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If a and b are the numbers, then (a+b)2 = a2 + 2ab + b2, which is different from a2 + b2 (not necessarily larger). The two quantities are equal only when one (or both) of a,b is zero.
Wiki User
∙ 12y ago
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5
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sum of squares: 32 + 52 = 9 + 25 = 34 square of sum (3 + 5)2 = 82 = 64 This is a version of the Cauchy-Schwarz inequality.
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