What is the value of $$1006^2 - 1007 \times 1005 + 1008 \times 1004 - 1009 \times 1003$$?
$$1006^2-1007\times1005+1008\times1004-1009\times1003$$
$$=1006^2-\left(1006^2-1\right)+\left(1006^2-2^2\right)-\left(1006^2-3^2\right)$$
$$=1006^2-1006^2+1+1006^2-4-1006^2+9\ .$$
$$=10-4\ .$$
$$=6\ .$$
A is correct choice.
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