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$\frac12\{(a+b)^2-(a-b)^2\}$

$=\frac12\{(a^2+2ab+b^2)-(a^2-2ab+b^2)\}$

$=\frac12\left(a^2+2ab+b^2-a^2+2ab-b^2\right)$

$=\frac12\cdot4ab$

$=2ab$

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