一、裂差(母积子差) ①b−aa×b=1a−1b 如:8−77×8=17−18 ②b2−a2a×b=ba−ab 如:72−626×7=76−67 ③1n(n+k)=1k1n−1n+k 如:13×(3+2)=1213−15 ④2n(n+1)(n+2)=1n(n+1)−1(n+1)(n+2) 如:21×2×3=11×2−12×3 ⑤4(2n−1)(2n+1)(2n+3)=1(2n−1)(2n+1)−1(2n+1)(2n+3) 如:41×3×5=11×3−13×5