AIME Problem 1

Algebra Level 3

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

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