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GDP at factor prices

Does anyone know what the logic is to arriving at GDP at factor prices, from market prices? As I understand it, many market prices include some sort of tax (VAT) and/or subsidy, so that 'actual price' should equal market price + whatever tax. Anyway, below is the formula from the book. Do you know why you subtract the tax and add the subsidy?

Thanks

GDP at market prices
– indirect taxes
+ subsidies
=
GDP at factor prices

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