用因式分解的办法做简便计算（1）22.4^2-27.6^2（2）2.03*2.5+4.83*2.5+3.14*2.5（3）1.25*14^2-125*8.6^2（4）102^2-2*(100^2-2^2)+98^2（5）27*1.8^2-12*1.2^2（6）(1-1/2^2)(1-1/3^2)(1-1/4^2)……(1-1/2008^2)

（1）22.4^2-27.6^2
=(22.4+27.6)(22.4-27.6)=-5.2*50=-260
（2）2.03*2.5+4.83*2.5+3.14*2.5
=2.5(2.03+4.83+3.14)
=2.5*10
=25
（3）1.25*14^2-125*8.6^2
=1.25(14^2-86^2)
=1.25(14+86)(14-86)
=1.25*100*(-72)
=-125*72
=-125*8*9
=-1000*9
=-9000
（4）102^2-2*(100^2-2^2)+98^2
=102^2-2*100^2+2*2^2+98^2
=(102+100)(102-100)+(98+100)(98-100)+2*2^2
=202*2-198*2+2*2^2
=2*(202-198)+2*2^2
=8+8
=16
（5）27*1.8^2-12*1.2^2
（6）(1-1/2^2)(1-1/3^2)(1-1/4^2)……(1-1/2008^2)

（1）22.4^2-27.6^2 =(22.4+27.6)(22.4-27.6)=50*(-5.2)=-260
（2）2.03*2.5+4.83*2.5+3.14*2.5 =2.5(2.03+4.83+3.14)=2.5*11=2.5*10=25
（3）1.25*14^2-125*8.6^2 =1.25(14^2-86^2)=1.25(14+86)(14-86)=125*(-72)=-9000
（4）102^2-2*(100^2-2^2)+98^2 =(102^2-100^2)+(98^2-100^2)+2^3=(102+100)(102-100)+(98-100)(98+100)+2^3=2(202-198+4)=16
（5）27*1.8^2-12*1.2^2 3*(9*1.8^2-4*1.2^2)=3*(5.4+2.4)(5.4-2.4)=70.2
（6）(1-1/2^2)(1-1/3^2)(1-1/4^2)……(1-1/2008^2)
因为1/n^2=(1+n)(n-1)/n^2所有经叠加后原式等于=（1*2009）/（2*2008）=2009/4016

(1)原式=(22.4-27.6)(22.4+27.6)
=(-5.2)*50
=-260
(2)原式=(2.03+4.83+3.14)*2.5
=10*2.5
=25
(3)原式=5(0.5*14-5*8.6)(0.5*14+5*8.6)
=5(7-43)(7+43)
=5*(-36)*50
=-9000
(4)原式=102^2-2*(100-2)(100+2)+98^2
=(102-98)^2
=16
(5)原式=3(3*1.8-2*1.2)(3*1.8+2*1.2)
=3*3*7.8
=70.2
(6)原式=(1-1/2)(1+1/2)(1-1/3)(1+1/3)……(1-1/2008)(1+1/2008)
=(1/2)*(3/2)*(2/3)*(4/3)*……*(2007/2008)(2009/2008)
=(1/2)*(2009/2008)
=2009/4016

(1) 原式=(22.4+27.6)*(22.4-27.6)
=50*(-5.2)
=-260
(2) 原式=2.5*(2.03+4.83+3.14)
=2.5*10
=25
(4) 原式=(100+2)^2-2[(100+2)*(100-2)]+(100-2)^2
=[(100+2)-(100-2)]^2
=4^2
=16

1.22.4^2-27.6^2=(22.4+27.6)(22.4-27.6)=50*(-5.2)=-27
2.=(2.03+4.83+3.14)*2.5=8*2.5=20
3.=125*(1.4^2-8.6^2)=125*(1.4+8.6)(1.4-8.6)=-900
4.=102^2-2*(100+2)(100-2)+98^2=(102-98)^2=4^2=16
5.=3*(9*1.8^2-4*1.2^2)=3*(5.4+2.4)(5.4-2.4)=70.2
6.=(1/2)*(3/2)*(2/3)*(4/3)*……*(2007/1008)*(2009/2008)
=(1/2)*(2009/2008)=2009/4016