(1/2a-1/2b)(1/3a+1/3b)+b^2

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(1/2a-1/2b)(1/3a+1/3b)+b^2

=1/2(a-b)×1/3(a+b)+b²
=1/6(a-b)(a+b)+b²
=1/6(a²-b²)+b²
=a²/6 -b²/6+ b²
=a²/6 +5b²/6