The coefficient of x5 in the expansion of (1+2x)6(1−x)7 is

(1+2x)6(1−x)7=1+6C1(2x)+6C2(2x)2+6C3(2x)3+6C4(2x)4+6C5(2x)5+6C6(2x)6×1−7C1x+7C2x2−7C3x3+7C4x4…=1+12x+60x2+160x3+240x4+192x5+…×1−7x+21x2−35x3+35x4−21x5+…∴ Coefficient of x5 in the expansion of (1+2x)6(1−x)7=1×(−21)+12×35+60×(−35) +160×21+240×(−7)+192=−21+420−2100+3360−1680+192=171