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square of sum∗ pahio† 2013-03-21 19:44:50 The well-known formula for squaring a sum of two numbers or terms is (a+b)2 = a2 +2ab+b2 . (1) It may be derived by multiplying the binomial a+b by itself. Similarly one can get the squaring formula for a sum of three summands: (a+b+c)2 = a2 +b2 +c2 +2bc+2ca+2ab (2) Its contents may be expressed as the Rule. The square of a sum is equal to the sum of the squares of all the summands plus the sum of all the double products of the summands in twos: !2 X ai = X i i a2i + 2 X ai aj . i<j This is true for any number of summands. The rule may be formulated also as (a+b+c + ...)2 = (a)a + (2a+b)b + (2a+2b+c)c + ... (3) which in the case of four summands is (a+b+c+d)2 = (a)a + (2a+b)b + (2a+2b+c)c + (2a+2b+2c+d)d. (4) One can use the idea of (3) to find the square root of a polynomial, when one tries to arrange the polynomial into the form of the right hand side of (3). ∗ hSquareOfSumi created: h2013-03-21i by: hpahioi version: h37427i Privacy setting: h1i hTopici h30-00i h26-00i h11-00i † This text is available under the Creative Commons Attribution/Share-Alike License 3.0. You can reuse this document or portions thereof only if you do so under terms that are compatible with the CC-BY-SA license. 1