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①2008×2010×(12008×2009+12009×2010)

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①2008×2010×(
1
2008×2009
+
1
2009×2010
①2008×2010×(12008×2009+12009×2010)
①2008×2010×(
1
2008×2009+
1
2009×2010)
=2008×2010×
1
2008×2009+2008×2010×
1
2009×2010,
=
2010
2009+
2008
2009,
=
4018
2009,
=2.
②2000×20102010-2010×20002000
=2000×2010×10001-2010×2000×10001,
=0;

9
15×
14
17+
8
17×
14
15
=
9
15×
14
17+
1
17×14(
1
15×8),
=
9
15×
4
17+
14
17×
8
15,
=(
9
15+
8
15)×
14
17,
=
17
15×
14
17,
=
14
15;
④1×2+2×3+3×4+4×5+…+18×19+19×20
=12+1+22+2+32+3+…+192+19
=12+22+32+…+192+1+2+…+19,
=19×(19+1)×(19×2+1)÷6+(19+1)×19÷2,
=19×20×39÷6+20×19÷2,
=2470+190,
=2660.