原式= (40+1/3)(39+2/3)=(40+1/3)(40-1/3)=1600-1/9
2014²－2015×293=2014²－2015×293-1+1
=(2014+1)(2014-1)－2015×293+1
=2015x2013 －2015×293+1
=2015(2013-293) + 1 = 2015x1720 + 1
3、解 9x11x101+1 = 99x101 + 1= (100-1)(100+1) +1 = 10000-1+1 = 10000
5﹙a－2b﹚﹙1/5a＋2/5b﹚=5x1/5 (a - 2b)(a + 2b) =a² - 4b²
(﹣3a＋b﹚﹙﹣2b＋3a﹚＋4b² = 4b² -(3a-b)(3a-2b)
= 4b² -(9a²-9ab+2b²)
=2b² -9a²+9ab
=(b+3a)(b-3a)+b(b+3a)+6ab
=(b+3a)(2b-3a)+6ab
﹙x＋y﹚²－﹙x－y﹚² = (x+y+x-y)(x+y-x+y) = 4xy
25²－24² =(24+1)²－24² = (24+1+24)(24+1-24) = 49
﹙1-1/2²﹚﹙1－1/3²﹚﹙1－1/4²﹚...﹙1－1/9²﹚﹙1－1/10²﹚=(1+1/2)(1-1/2)(1+1/3)(1-1/3)(1+1/4)(1-1/4).(1+1/9)(1-1/9)(1+1/10)(1-1/10)
=(3/2)(1/2)(4/3)(2/3)(5/4)(3/4).(10/9)(8/9)(11/10)(9/10)
=[(3/2)(4/3)(5/4)..,(10/9)(11/10)][(1/2)(2/3)(3/4).(8/9)(9/10)]
=(11/2)(1/10) = 11/20
﹙a＋b﹚²＝16 ,a²+b²+2ab ＝16 （1）
﹙a－b﹚²＝8 a²+b²-2ab ＝8 （2）
(1) - (2) 得：4ab = 8 解得：ab = 2
(﹣a－2b)(2a－b)－(a－2b)(b＋2a) = (a+2b)(b－2a)－(a－2b)(b＋2a)
=(-2a²-3ab+2b²) - (2a²-3ab-2b²) = 4b²-4a² = 4(b+a)(b-a)
太晚了,我在替你寫作業(yè)啊!剩下的很簡單,你仿照上面的方法可以做出來的!