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Positive Difference Between A and B

Source: 2015 AIME I Problem 1

March 20, 2015
AMCAIMEAIME I

Problem Statement

The expressions A=1×2+3×4+5×6+⋯+37×38+39A=1\times2+3\times4+5\times6+\cdots+37\times38+39 and B=1+2×3+4×5+⋯+36×37+38×39B=1+2\times3+4\times5+\cdots+36\times37+38\times39 are obtained by writing multiplication and addition operators in an alternating pattern between successive integers. Find the positive difference between integers AA and BB.
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