Question: One proof of the Pythagorean Theorem involves expressing algebraically the areas of the two squares given below and equating the results. Notice that each contains copies of a right triangle with legs measuring \(a\) and \(b\) and hypotenuse measuring \(c\). Note that both squares have sides of length \(a+b\) making both areas \((a+b)^{2}\). Using this information, show that \(a^{2}+b^{2}=c^{2}\).

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