Equation Puzzle

A nucleotide composition constraint of genome sequences. Zhang CT, Zhang R. Comput Biol Chem. 2004 Apr;28(2):149-53. PMID: 15130543

For the base frequences in a DNA a, c, g, t, they define:

S = a2 + c2 + g2 + t2

Then they claim:

S = ½ + ½ (a - t)2 + ½ (g - c)2 - (a + t)(g + c)

Your challenge: Prove their claim.

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origin:    2009 Jan 31
updated: 2009 Feb 01

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